## Set-Valued and Variational Analysis

### Theory and Applications

 Short Title: Set-Valued Var. Anal. Publisher: Springer Netherlands, Dordrecht ISSN: 1877-0533; 1877-0541/e Online: http://link.springer.com/journal/volumesAndIssues/11228 Predecessor: Set-Valued Analysis Comments: Indexed cover-to-cover
 Documents Indexed: 532 Publications (since 2009) References Indexed: 515 Publications with 15,287 References.
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### Latest Issues

 30, No. 3 (2022) 30, No. 2 (2022) 30, No. 1 (2022) 29, No. 4 (2021) 29, No. 3 (2021) 29, No. 2 (2021) 29, No. 1 (2021) 28, No. 4 (2020) 28, No. 3 (2020) 28, No. 2 (2020) 28, No. 1 (2020) 27, No. 4 (2019) 27, No. 3 (2019) 27, No. 2 (2019) 27, No. 1 (2019) 26, No. 4 (2018) 26, No. 3 (2018) 26, No. 2 (2018) 26, No. 1 (2018) 25, No. 4 (2017) 25, No. 3 (2017) 25, No. 2 (2017) 25, No. 1 (2017) 24, No. 4 (2016) 24, No. 3 (2016) 24, No. 2 (2016) 24, No. 1 (2016) 23, No. 4 (2015) 23, No. 3 (2015) 23, No. 2 (2015) 23, No. 1 (2015) 22, No. 4 (2014) 22, No. 3 (2014) 22, No. 2 (2014) 22, No. 1 (2014) 21, No. 4 (2013) 21, No. 3 (2013) 21, No. 2 (2013) 21, No. 1 (2013) 20, No. 4 (2012) 20, No. 3 (2012) 20, No. 2 (2012) 20, No. 1 (2012) 19, No. 4 (2011) 19, No. 3 (2011) 19, No. 2 (2011) 19, No. 1 (2011) 18, No. 3-4 (2010) 18, No. 2 (2010) 18, No. 1 (2010) 17, No. 4 (2009) 17, No. 3 (2009) 17, No. 2 (2009) 17, No. 1 (2009)
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### Authors

 12 Mordukhovich, Boris S. 11 Bauschke, Heinz H. 11 López-Cerdá, Marco Antonio 10 Outrata, Jiří V. 10 Wang, Shawn Xianfu 10 Zaslavski, Alexander Yakovlevich 8 Henrion, René 8 Kruger, Alexander Y. 8 Théra, Michel A. 8 Zhang, Liwei 7 Adly, Samir 7 Burachik, Regina Sandra 7 Gfrerer, Helmut 7 Hantoute, Abderrahim 7 Martínez-Legaz, Juan-Enrique 7 Thibault, Lionel 7 Ye, Jane J. 6 Borwein, Jonathan Michael 6 Boţ, Radu Ioan 6 Combettes, Patrick L. 6 Goberna, Miguel Angel 6 Yao, Jen-Chih 5 Arutyunov, Aram Vladimirovic 5 Aussel, Didier 5 Beer, Gerald Alan 5 Cánovas, María Josefa 5 Castaing, Charles 5 de Pinho, Maria do Rosário 5 Mehlitz, Patrick 5 Nam, Nguyen Mau 5 Penot, Jean-Paul 5 Reich, Simeon 5 Seeger, Alberto 5 Simons, Stephen 5 Valero, José 5 Volle, Michel 4 Aragón Artacho, Francisco Javier 4 Benko, Matus 4 Bianchi, Monica 4 Bounkhel, Messaoud 4 Červinka, Michal 4 Cibulka, Radek 4 Csetnek, Ernö Robert 4 Dontchev, Asen L. 4 Eberhard, Andrew C. 4 Fabian, Marián J. 4 Ivanov, Grigorii E. 4 Li, Shengjie 4 Luke, David Russell 4 Noll, Dominikus 4 Parra, Juan 4 Pini, Rita 4 Smirnov, Georgi V. 4 Soubeyran, Antoine 4 Uderzo, Amos 4 Van Ackooij, Wim 4 Wachsmuth, Gerd 4 Yao, Liangjin 3 Attouch, Hedy 3 Azzam-Laouir, Dalila 3 Burke, James V. 3 Colombo, Giovanni 3 Correa, Rafael 3 Daniilidis, Aris 3 de Oliveira, Welington Luis 3 Donchev, Tzanko Donchev 3 Durea, Marius 3 Hintermüller, Michael 3 Hoheisel, Tim 3 Huang, Hui 3 Huynh Van Ngai 3 Izmailov, Alekseĭ F. 3 Kassay, Gábor 3 Lassonde, Marc 3 Le, Ba Khiet 3 Liu, Yulan 3 Malick, Jérôme 3 Meng, Kaiwen 3 Miglierina, Enrico 3 Movahedian, Nooshin 3 Pan, Shaohua 3 Pang, Liping 3 Pérez-Aros, Pedro 3 Phan Quôc Khánh 3 Phan, Hung M. 3 Pištěk, Miroslav 3 Revalski, Julian Petrov 3 Ribarska, Nadezhda K. 3 Roberto, Lucchetti E. 3 Rockafellar, Ralph Tyrrell 3 Royset, Johannes O. 3 Sagara, Nobusumi 3 Sagastizábal, Claudia A. 3 Sagastizábal, Claudia S. 3 Shanbhag, Uday V. 3 Strugariu, Radu 3 Toledo, Fco. Javier 3 Vilches, Emilio 3 Voisei, Mircea Dan 3 Wang, Bingwu ...and 566 more Authors
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### Fields

 309 Calculus of variations and optimal control; optimization (49-XX) 244 Operations research, mathematical programming (90-XX) 129 Operator theory (47-XX) 66 Functional analysis (46-XX) 63 Numerical analysis (65-XX) 61 Ordinary differential equations (34-XX) 42 General topology (54-XX) 40 Real functions (26-XX) 34 Partial differential equations (35-XX) 32 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 30 Convex and discrete geometry (52-XX) 30 Global analysis, analysis on manifolds (58-XX) 23 Systems theory; control (93-XX) 22 Measure and integration (28-XX) 20 Dynamical systems and ergodic theory (37-XX) 13 General and overarching topics; collections (00-XX) 12 Approximations and expansions (41-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 8 History and biography (01-XX) 8 Probability theory and stochastic processes (60-XX) 6 Difference and functional equations (39-XX) 5 Computer science (68-XX) 5 Mechanics of deformable solids (74-XX) 5 Information and communication theory, circuits (94-XX) 3 Mathematical logic and foundations (03-XX) 3 Algebraic geometry (14-XX) 2 Topological groups, Lie groups (22-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Biology and other natural sciences (92-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Integral equations (45-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX)

### Citations contained in zbMATH Open

395 Publications have been cited 2,736 times in 2,146 Documents Cited by Year
Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators. Zbl 1284.47043
Combettes, Patrick L.; Pesquet, Jean-Christophe
2012
Error bounds: necessary and sufficient conditions. Zbl 1192.49018
Fabian, Marian J.; Henrion, René; Kruger, Alexander Y.; Outrata, Jiří V.
2010
A three-operator splitting scheme and its optimization applications. Zbl 1464.47041
Davis, Damek; Yin, Wotao
2017
On directional metric regularity, subregularity and optimality conditions for nonsmooth mathematical programs. Zbl 1321.49031
Gfrerer, Helmut
2013
Iterative methods for generalized split feasibility problems in Hilbert spaces. Zbl 1326.47099
Takahashi, Wataru; Xu, Hong-Kun; Yao, Jen-Chin
2015
Common solutions to variational inequalities. Zbl 1296.47060
Censor, Yair; Gibali, Aviv; Reich, Simeon; Sabach, Shoham
2012
A duality theory for set-valued functions. I: Fenchel conjugation theory. Zbl 1168.49031
Hamel, Andreas H.
2009
Resolvents of set-valued monotone vector fields in Hadamard manifolds. Zbl 1239.47043
Li, Chong; López, Genaro; Martín-Márquez, Victoria; Wang, Jin-Hua
2011
Multiple solutions for nonlinear coercive problems with a nonhomogeneous differential operator and a nonsmooth potential. Zbl 1258.35075
Gasiński, Leszek; Papageorgiou, Nikolaos S.
2012
Generic existence and approximation of fixed points for nonexpansive set-valued maps. Zbl 1183.47055
de Blasi, Francesco S.; Myjak, Józef; Reich, Simeon; Zaslavski, Alexander J.
2009
Restricted normal cones and the method of alternating projections: theory. Zbl 1272.49027
Bauschke, Heinz H.; Luke, D. Russell; Phan, Hung M.; Wang, Xianfu
2013
Dualization of signal recovery problems. Zbl 1229.90123
Combettes, Patrick L.; Dũng, Đinh; Vũ, Băng Công
2010
Error bounds and Hölder metric subregularity. Zbl 1330.49012
Kruger, Alexander Y.
2015
On global attractors of multivalued semiflows generated by the 3D Bénard system. Zbl 1259.35042
Kapustyan, Alexey V.; Pankov, Andrey V.; Valero, José
2012
Firmly nonexpansive mappings and maximally monotone operators: correspondence and duality. Zbl 1263.47066
Bauschke, Heinz H.; Moffat, Sarah M.; Wang, Xianfu
2012
Robust duality in parametric convex optimization. Zbl 1327.90195
Boţ, R. I.; Jeyakumar, V.; Li, G. Y.
2013
A second-order model for image denoising. Zbl 1203.94006
Bergounioux, Maïtine; Piffet, Loic
2010
Discrete approximations of a controlled sweeping process. Zbl 1312.49015
Colombo, G.; Henrion, R.; Hoang, N. D.; Mordukhovich, B. S.
2015
Forward-backward and Tseng’s type penalty schemes for monotone inclusion problems. Zbl 1308.47064
Boţ, Radu Ioan; Csetnek, Ernö Robert
2014
Calculus rules for derivatives of multimaps. Zbl 1173.54008
Li, S. J.; Meng, K. W.; Penot, J.-P.
2009
First and second order convex sweeping processes in reflexive smooth Banach spaces. Zbl 1200.34067
Bounkhel, Messaoud; Al-Yusof, Rabab
2010
A maximum principle for the controlled sweeping process. Zbl 1398.49015
Arroud, Chems Eddine; Colombo, Giovanni
2018
About subtransversality of collections of sets. Zbl 1383.49028
Kruger, Alexander Y.; Luke, D. Russell; Thao, Nguyen H.
2017
Regularity of weak solutions and their attractors for a parabolic feedback control problem. Zbl 1327.35468
Kasyanov, Pavlo O.; Toscano, Luisa; Zadoianchuk, Nina V.
2013
Codifferential calculus. Zbl 1262.47074
Li, Shengjie; Penot, Jean-Paul; Xue, Xiaowei
2011
Generalized control systems in the space of probability measures. Zbl 1400.93330
Cavagnari, Giulia; Marigonda, Antonio; Nguyen, Khai T.; Priuli, Fabio S.
2018
Restricted normal cones and the method of alternating projections: applications. Zbl 1349.65191
Bauschke, Heinz H.; Luke, D. Russell; Phan, Hung M.; Wang, Xianfu
2013
Variational analysis of directional minimal time functions and applications to location problems. Zbl 1321.49028
Nam, Nguyen Mau; Zălinescu, Constantin
2013
Calmness of the feasible set mapping for linear inequality systems. Zbl 1297.90163
Cánovas, M. J.; López, M. A.; Parra, J.; Toledo, F. J.
2014
On metric pseudo-(sub)regularity of multifunctions and optimality conditions for degenerated mathematical programs. Zbl 1297.49023
Gfrerer, Helmut
2014
On subregularity properties of set-valued mappings. Zbl 1285.90062
Apetrii, Marius; Durea, Marius; Strugariu, Radu
2013
Cutting plane oracles to minimize non-smooth non-convex functions. Zbl 1219.49013
Noll, Dominikus
2010
A shared-constraint approach to multi-leader multi-follower games. Zbl 1307.91046
Kulkarni, Ankur A.; Shanbhag, Uday V.
2014
A proximal point-type method for multicriteria optimization. Zbl 1296.90113
Bento, G. C.; Neto, J. X. Cruz; Soubeyran, A.
2014
Inradius and circumradius of various convex cones arising in applications. Zbl 1217.46047
Henrion, René; Seeger, Alberto
2010
Fixed points and variational principles with applications to capability theory of wellbeing via variational rationality. Zbl 1318.49029
Bao, T. Q.; Mordukhovich, B. S.; Soubeyran, A.
2015
About intrinsic transversality of pairs of sets. Zbl 1387.49023
Kruger, Alexander Y.
2018
Solving ill-posed bilevel programs. Zbl 1362.90346
Zemkoho, Alain B.
2016
Clarke generalized Jacobian of the projection onto symmetric cones. Zbl 1168.49043
Kong, Lingchen; Tunçel, Levent; Xiu, Naihua
2009
Optimal control involving sweeping processes. Zbl 1419.49030
de Pinho, M. d. R.; Ferreira, M. M. A.; Smirnov, G. V.
2019
On properties of different notions of centers for convex cones. Zbl 1198.46011
Henrion, René; Seeger, Alberto
2010
Second-order optimality conditions for a semilinear elliptic optimal control problem with mixed pointwise constraints. Zbl 1368.49023
Kien, B. T.; Nhu, V. H.; Son, N. H.
2017
Deep neural network structures solving variational inequalities. Zbl 1448.49014
Combettes, Patrick L.; Pesquet, Jean-Christophe
2020
Properties of chance constraints in infinite dimensions with an application to PDE constrained optimization. Zbl 1410.90135
Farshbaf-Shaker, M. H.; Henrion, R.; Hömberg, D.
2018
Local search proximal algorithms as decision dynamics with costs to move. Zbl 1209.49042
Attouch, H.; Soubeyran, A.
2011
Convergence properties of a smoothing approach for mathematical programs with second-order cone complementarity constraints. Zbl 1261.90058
Zhang, Yi; Zhang, Liwei; Wu, Jia
2011
A class of generalized evolutionary problems driven by variational inequalities and fractional operators. Zbl 1441.47076
Migórski, Stanisław; Zeng, Shengda
2019
Perturbed evolution problems with continuous bounded variation in time and applications. Zbl 1403.34046
Azzam-Laouir, Dalila; Castaing, Charles; Monteiro Marques, M. D. P.
2018
(Sub-)differentiability of probability functions with elliptical distributions. Zbl 1416.90028
van Ackooij, W.; Aleksovska, I.; Munoz-Zuniga, M.
2018
Uniform continuity, uniform convergence, and shields. Zbl 1236.54012
Beer, Gerald; Levi, Sandro
2010
Asymptotics for some proximal-like method involving inertia and memory aspects. Zbl 1214.65037
Cabot, Alexandre; Frankel, Pierre
2011
Graphical derivatives and stability analysis for parameterized equilibria with conic constraints. Zbl 1330.49013
Mordukhovich, Boris S.; Outrata, Jiri V.; Ramírez C., Héctor
2015
Nonlocal problems for differential inclusions in Hilbert spaces. Zbl 1312.34097
Benedetti, I.; Loi, N. V.; Malaguti, L.
2014
On stochastic mirror-prox algorithms for stochastic Cartesian variational inequalities: randomized block coordinate and optimal averaging schemes. Zbl 07002699
Yousefian, Farzad; Nedić, Angelia; Shanbhag, Uday V.
2018
On the theory of global attractors and Lyapunov functionals. Zbl 1260.37048
Coti Zelati, Michele
2013
On optimality conditions in control of elliptic variational inequalities. Zbl 1211.49036
Outrata, Jiří; Jarušek, Jiří; Stará, Jana
2011
Three solutions for a partial differential inclusion via nonsmooth critical point theory. Zbl 1219.35381
Iannizzotto, Antonio
2011
Infimum gaps for limit solutions. Zbl 1311.49087
Aronna, M.-Soledad; Motta, Monica; Rampazzo, Franco
2015
Gradient consistency for integral-convolution smoothing functions. Zbl 1321.49027
Burke, James V.; Hoheisel, Tim; Kanzow, Christian
2013
Flow invariance on stratified domains. Zbl 1327.93215
Barnard, Richard C.; Wolenski, Peter R.
2013
Mathematical programs with semidefinite cone complementarity constraints: constraint qualifications and optimality conditions. Zbl 1296.90118
Wu, Jia; Zhang, Liwei; Zhang, Yi
2014
Mixed semicontinuous perturbation of nonconvex state-dependent sweeping process. Zbl 1307.34033
Azzam-Laouir, Dalila; Izza, Sabrina; Thibault, Lionel
2014
Subgradients of the value function to a parametric optimal control problem. Zbl 1214.47064
Toan, N. T.; Kien, B. T.
2010
The limiting normal cone to pointwise defined sets in Lebesgue spaces. Zbl 1401.49018
Mehlitz, Patrick; Wachsmuth, Gerd
2018
On proximal subgradient splitting method for minimizing the sum of two nonsmooth convex functions. Zbl 1365.65160
Bello Cruz, José Yunier
2017
Metric regularity of mappings and generalized normals to set images. Zbl 1218.49023
Mordukhovich, Boris S.; Nam, Nguyen Mau; Wang, Bingwu
2009
Well-posedness of minimal time problems with constant dynamics in Banach spaces. Zbl 1219.49014
Colombo, Giovanni; Goncharov, Vladimir V.; Mordukhovich, Boris S.
2010
Variational geometric approach to generalized differential and conjugate calculi in convex analysis. Zbl 1392.49019
Mordukhovich, B. S.; Nam, N. M.; Rector, R. B.; Tran, T.
2017
Necessary optimality conditions for mathematical programs with second-order cone complementarity constraints. Zbl 1297.90152
Liang, Yan-Chao; Zhu, Xi-De; Lin, Gui-Hua
2014
Equilibrium problems: existence results and applications. Zbl 06861473
Cotrina, John; García, Yboon
2018
Global solutions for nonlinear delay evolution inclusions with nonlocal initial conditions. Zbl 1266.34127
Vrabie, Ioan I.
2012
Equivalent conditions for local error bounds. Zbl 1254.49011
Meng, K. W.; Yang, X. Q.
2012
The Josephy-Newton method for semismooth generalized equations and semismooth SQP for optimization. Zbl 1285.90065
Izmailov, Alexey F.; Kurennoy, Alexey S.; Solodov, Mikhail V.
2013
On some regularity properties in variational analysis. Zbl 1177.49032
Uderzo, Amos
2009
New formulas for the Fenchel subdifferential of the conjugate function. Zbl 1205.26018
Correa, Rafael; Hantoute, Abderrahim
2010
Infinite horizon optimal control problems in the light of convex analysis in Hilbert spaces. Zbl 1311.49084
Pickenhain, Sabine
2015
Fixed points, fixed sets and iterated multifunction systems for nonself multivalued operators. Zbl 1328.54047
2015
Finite convergence of the proximal point algorithm for variational inequality problems. Zbl 1321.49016
Matsushita, Shin-Ya; Xu, Li
2013
A characterization of the subdifferential of singular Gaussian distribution functions. Zbl 1327.90159
van Ackooij, Wim; Minoux, M.
2015
Stability and optimality of solutions to differential inclusions via averaging method. Zbl 1307.34001
Gama, Ricardo; Smirnov, Georgi
2014
An inertial algorithm for DC programming. Zbl 1434.90151
de Oliveira, Welington; Tcheou, Michel P.
2019
Dynamics of the Douglas-Rachford method for ellipses and $$p$$-spheres. Zbl 06913665
Borwein, Jonathan M.; Lindstrom, Scott B.; Sims, Brailey; Schneider, Anna; Skerritt, Matthew P.
2018
Necessary optimality conditions for optimal control problems with nonsmooth mixed state and control constraints. Zbl 1350.49027
Li, An; Ye, Jane J.
2016
Nonsmooth bundle trust-region algorithm with applications to robust stability. Zbl 1334.49092
Apkarian, Pierre; Noll, Dominikus; Ravanbod, Laleh
2016
Linear monotone subspaces of locally convex spaces. Zbl 1192.47047
Voisei, M. D.; Zălinescu, C.
2010
Convex inequalities without constraint qualification nor closedness condition, and their applications in optimization. Zbl 1231.90381
Dinh, N.; Goberna, M. A.; López, M. A.; Volle, M.
2010
Negatively invariant sets and entire trajectories of set-valued dynamical systems. Zbl 1225.37022
Kloeden, Peter E.; Marín-Rubio, Pedro
2011
Characterizing convexity of a function by its Fréchet and limiting second-order subdifferentials. Zbl 1209.49031
Chieu, N. H.; Chuong, T. D.; Yao, J.-C.; Yen, N. D.
2011
A generalized inexact proximal point method for nonsmooth functions that satisfies Kurdyka Łojasiewicz inequality. Zbl 1342.49019
Bento, Glaydston C.; Soubeyran, Antoine
2015
Strong and weak solutions to second order differential inclusions governed by monotone operators. Zbl 1315.34067
2014
State dependent sweeping process in $$p$$-uniformly smooth and $$q$$-uniformly convex Banach spaces. Zbl 1262.34072
Bounkhel, Messaoud; Castaing, Charles
2012
Attractors for multi-valued non-autonomous dynamical systems: relationship, characterization and robustness. Zbl 1401.37085
Cui, Hongyong; Langa, José A.; Li, Yangrong; Valero, José
2018
Uniform continuity and a new bornology for a metric space. Zbl 1422.54019
Beer, Gerald; Garrido, M. Isabel; Meroño, Ana S.
2018
Any semitopological group that is homeomorphic to a product of Čech-complete spaces is a topological group. Zbl 1321.22006
Moors, Warren B.
2013
Strong stationarity for optimization problems with complementarity constraints in absence of polyhedricity. With applications to optimization with semidefinite and second-order-cone complementarity constraints. Zbl 1368.49018
Wachsmuth, Gerd
2017
Solving stochastic programming problems with risk measures by progressive hedging. Zbl 1416.90027
Rockafellar, R. Tyrrell
2018
Nonsmooth Lur’e dynamical systems in Hilbert spaces. Zbl 1333.37113
Adly, Samir; Hantoute, Abderrahim; Le, Ba Khiet
2016
Constraint qualifications for nonsmooth mathematical programs with equilibrium constraints. Zbl 1191.90070
Movahedian, N.; Nobakhtian, S.
2009
Generalized topological essentiality and coincidence points of multivalued maps. Zbl 1182.54052
Gabor, Grzegorz; Górniewicz, Lech; Ślosarski, Mirosław
2009
Pareto solutions of polyhedral-valued vector optimization problems in Banach spaces. Zbl 1177.49033
Zheng, Xi Yin
2009
Perturbation techniques for convergence analysis of proximal gradient method and other first-order algorithms via variational analysis. Zbl 1487.90643
Wang, Xiangfeng; Ye, Jane J.; Yuan, Xiaoming; Zeng, Shangzhi; Zhang, Jin
2022
Calmness and calculus: two basic patterns. Zbl 1484.49026
Benko, Matúš; Mehlitz, Patrick
2022
The obstacle problem at zero for the fractional $$p$$-Laplacian. Zbl 07490854
Frassu, Silvia; Rocha, Eugénio M.; Staicu, Vasile
2022
Metric regularity and Lyusternik-Graves theorem via approximate fixed points of set-valued maps in noncomplete metric spaces. Zbl 1484.49030
Ait Mansour, Mohamed; Bahraoui, Mohamed Amin; El Bekkali, Adham
2022
Kantorovich’s fixed point theorem and coincidence point theorems for mappings in vector metric spaces. Zbl 07536248
Arutyunov, Aram V.; Zhukovskiy, Evgeny S.; Zhukovskiy, Sergey E.; Zhukovskaya, Zukhra T.
2022
First-order frameworks for continuous Newton-like dynamics governed by maximally monotone operators. Zbl 07536249
Labarre, Florian; Maingé, Paul-Emile
2022
Distance function associated to a prox-regular set. Zbl 07536262
Nacry, Florent; Thibault, Lionel
2022
On ranges of non-linear operators. Zbl 07536265
2022
A direct proof of convergence of Davis-Yin splitting algorithm allowing larger stepsizes. Zbl 07563237
Aragón-Artacho, Francisco J.; Torregrosa-Belén, David
2022
Variational analysis perspective on linear convergence of some first order methods for nonsmooth convex optimization problems. Zbl 1484.90082
Ye, Jane J.; Yuan, Xiaoming; Zeng, Shangzhi; Zhang, Jin
2021
A reflected forward-backward splitting method for monotone inclusions involving Lipschitzian operators. Zbl 1481.47082
Cevher, Volkan; Vũ, Bằng Công
2021
Transversality properties: primal sufficient conditions. Zbl 1470.49029
Cuong, Nguyen Duy; Kruger, Alexander Y.
2021
No infimum gap and normality in optimal impulsive control under state constraints. Zbl 1470.49064
Fusco, Giovanni; Motta, Monica
2021
Continuous Newton-like inertial dynamics for monotone inclusions. Zbl 1477.37101
Attouch, Hedy; László, Szilárd Csaba
2021
BV continuous solutions of an evolution inclusion with maximal monotone operator and nonconvex-valued perturbation. Existence theorem. Zbl 1482.34144
Tolstonogov, A. A.
2021
New inertial factors of the Krasnosel’skiĭ-Mann iteration. Zbl 07345313
Dong, Yunda
2021
The gradient projection algorithm for smooth sets and functions in nonconvex case. Zbl 1473.90124
Balashov, Maxim V.
2021
Regularization of Brézis pseudomonotone variational inequalities. Zbl 1462.49033
Bianchi, M.; Kassay, G.; Pini, R.
2021
On a time and state dependent maximal monotone operator coupled with a sweeping process with perturbations. Zbl 1469.34057
Benguessoum, Messaouda; Azzam-Laouir, Dalila; Castaing, Charles
2021
Upper semicontinuity of the solution map to a parametric elliptic optimal control problem. Zbl 1473.49031
Son, N. H.; Giang, N. B.
2021
Measure differential inclusions: existence results and minimum problems. Zbl 1479.34008
Di Piazza, Luisa; Marraffa, Valeria; Satco, Bianca
2021
Ergodic approach to robust optimization and infinite programming problems. Zbl 1473.90103
Pérez-Aros, Pedro
2021
On the analysis of variance-reduced and randomized projection variants of single projection schemes for monotone stochastic variational inequality problems. Zbl 1473.90097
Cui, Shisheng; Shanbhag, Uday V.
2021
Resolvents and Yosida approximations of displacement mappings of isometries. Zbl 1487.47080
Alwadani, Salihah; Bauschke, Heinz H.; Revalski, Julian P.; Wang, Xianfu
2021
On the positive definiteness of limiting coderivative for set-valued mappings. Zbl 1470.49034
Nghia, T. T. A.; Pham, D. T.; Tran, T. T. T.
2021
On the quantitative solution stability of parameterized set-valued inclusions. Zbl 1470.49035
Uderzo, A.
2021
Bregman forward-backward operator splitting. Zbl 1487.47097
Bùi, Minh N.; Combettes, Patrick L.
2021
Generalized sequential differential calculus for expected-integral functionals. Zbl 1472.49036
Mordukhovich, Boris S.; Pérez-Aros, Pedro
2021
Alternative representations of the normal cone to the domain of supremum functions and subdifferential calculus. Zbl 1482.46097
Correa, R.; Hantoute, A.; López, M. A.
2021
Enlargements of the Moreau-Rockafellar subdifferential. Zbl 1479.90195
Abbasi, Malek; Kruger, Alexander Y.; Théra, Michel
2021
Deep neural network structures solving variational inequalities. Zbl 1448.49014
Combettes, Patrick L.; Pesquet, Jean-Christophe
2020
Some results on strongly pseudomonotone quasi-variational inequalities. Zbl 1441.49013
Nguyen, Luong V.; Qin, Xiaolong
2020
Generalized derivatives for the solution operator of the obstacle problem. Zbl 1442.49030
Rauls, Anne-Therese; Wachsmuth, Gerd
2020
On a class of Lur’e dynamical systems with state-dependent set-valued feedback. Zbl 1451.37106
Le, Ba Khiet
2020
Some new characterizations of intrinsic transversality in Hilbert spaces. Zbl 1437.90152
Thao, Nguyen Hieu; Bui, Hoa T.; Cuong, Nguyen Duy; Verhaegen, Michel
2020
Duality for the robust sum of functions. Zbl 1476.90346
Dinh, N.; Goberna, M. A.; Volle, Michel
2020
New sharp necessary optimality conditions for mathematical programs with equilibrium constraints. Zbl 1491.90161
Gfrerer, Helmut; Ye, Jane J.
2020
Metric regularity of quasidifferentiable mappings and optimality conditions for nonsmooth mathematical programming problems. Zbl 1491.90167
Dolgopolik, M. V.
2020
The radius of metric subregularity. Zbl 1447.49030
Dontchev, Asen L.; Gfrerer, Helmut; Kruger, Alexander Y.; Outrata, Jiří V.
2020
Evolution inclusions governed by time-dependent maximal monotone operators with a full domain. Zbl 07243976
Vilches, Emilio; Nguyen, Bao Tran
2020
A discussion of probability functions and constraints from a variational perspective. Zbl 1467.90028
van Ackooij, Wim
2020
Finite alternation theorems and a constructive approach to piecewise polynomial approximation in Chebyshev norm. Zbl 1444.41004
Crouzeix, Jean-Pierre; Sukhorukova, Nadezda; Ugon, Julien
2020
Stability analysis for parameterized variational systems with implicit constraints. Zbl 1437.49017
Benko, Matúš; Gfrerer, Helmut; Outrata, Jiří V.
2020
An inverse mapping theorem in Fréchet-Montel spaces. Zbl 1446.49014
Cibulka, Radek; Fabian, Marián; Roubal, Tomáš
2020
Continuous dynamics related to monotone inclusions and non-smooth optimization problems. Zbl 1471.34123
Csetnek, Ernö Robert
2020
Bartle-Graves theorem revisited. Zbl 1444.47068
Dontchev, Asen L.
2020
A projection algorithm for non-monotone variational inequalities. Zbl 1434.90201
Burachik, Regina S.; Díaz Millán, R.
2020
On the stability of the directional regularity. Zbl 1442.47036
2020
On inexact relative-error hybrid proximal extragradient, forward-backward and Tseng’s modified forward-backward methods with inertial effects. Zbl 1445.90079
Alves, M. Marques; Marcavillaca, Raul T.
2020
Epi/hypo-convergence of bifunctions on general domains and approximations of quasi-variational problems. Zbl 1450.90052
Diem, H. T. H.; Khanh, P. Q.
2020
The ABC of DC programming. Zbl 1467.90037
de Oliveira, Welington
2020
Directional metric pseudo subregularity of set-valued mappings: a general model. Zbl 1439.49028
Van Ngai, Huynh; Tron, Nguyen Huu; Van Vu, Nguyen; Théra, Michel
2020
Immobile indices and CQ-free optimality criteria for linear copositive programming problems. Zbl 1442.90145
Kostyukova, O. I.; Tchemisova, T. V.; Dudina, O. S.
2020
The $$\mathcal{U}$$-Lagrangian, fast track, and partial smoothness of a prox-regular function. Zbl 1441.49020
Liu, Shuai; Eberhard, Andrew; Luo, Yousong
2020
Set-valued means. Zbl 1467.26019
Nikodem, Kazimierz
2020
A discussion on variational analysis in derivative-free optimization. Zbl 1473.49019
Hare, Warren
2020
Nonsmoothness in machine learning: specific structure, proximal identification, and applications. Zbl 07344790
Iutzeler, Franck; Malick, Jérôme
2020
Set-convergence and its application: a tutorial. Zbl 1464.49008
Royset, Johannes O.
2020
Optimal control involving sweeping processes. Zbl 1419.49030
de Pinho, M. d. R.; Ferreira, M. M. A.; Smirnov, G. V.
2019
A class of generalized evolutionary problems driven by variational inequalities and fractional operators. Zbl 1441.47076
Migórski, Stanisław; Zeng, Shengda
2019
An inertial algorithm for DC programming. Zbl 1434.90151
de Oliveira, Welington; Tcheou, Michel P.
2019
Sensitivity analysis for a class of $$H_{0}^{1}$$-elliptic variational inequalities of the second kind. Zbl 1416.35036
Christof, Constantin; Meyer, Christian
2019
Calculus for directional limiting normal cones and subdifferentials. Zbl 1426.49018
Benko, Matúš; Gfrerer, Helmut; Outrata, Jiří V.
2019
Connectedness of approximate efficient solutions for generalized semi-infinite vector optimization problems. Zbl 1430.90514
Peng, Zai-Yun; Wang, Xianfu; Yang, Xin-Min
2019
Dissipative and non-dissipative evolutionary quasi-variational inequalities with gradient constraints. Zbl 1418.35248
Hintermüller, M.; Rautenberg, C. N.; Strogies, N.
2019
About asymptotic analysis and set optimization. Zbl 07115100
Hernández, Elvira; López, Rubén
2019
On the sequential normal compactness condition and its restrictiveness in selected function spaces. Zbl 1428.49019
Mehlitz, Patrick
2019
On a method of solving some functional equations for set-valued functions. Zbl 1428.39032
Sikorska, Justyna
2019
Metric regularity properties in bang-bang type linear-quadratic optimal control problems. Zbl 1419.49012
Preininger, J.; Scarinci, T.; Veliov, V. M.
2019
Hölder error bounds and Hölder calmness with applications to convex semi-infinite optimization. Zbl 1430.49014
Kruger, Alexander Y.; López, Marco A.; Yang, Xiaoqi; Zhu, Jiangxing
2019
Sensitivity properties of parametric nonconvex evolution inclusions with application to optimal control problems. Zbl 1421.49002
2019
Progressive decoupling of linkages in optimization and variational inequalities with elicitable convexity or monotonicity. Zbl 07146007
Rockafellar, R. Tyrrell
2019
Inversion of nonsmooth maps between Banach spaces. Zbl 1433.49021
Jaramillo, Jesús A.; Lajara, Sebastián; Madiedo, Óscar
2019
Theorems of the alternative for systems of convex inequalities. Zbl 07058435
Arutyunov, Aram V.; Zhukovskiy, Sergey E.; Marinkovic, Boban
2019
Continuity of the metric projection and local solar properties of sets. Continuity of the metric projection and local solar properties of sets, continuity of the metric projection and solar properties. Zbl 1423.41050
Alimov, A. R.
2019
Analysis of optimal control problems of semilinear elliptic equations by BV-functions. Zbl 1421.35124
Casas, Eduardo; Kunisch, Karl
2019
Convergence analysis of the implicit Euler-discretization and sufficient conditions for optimal control problems subject to index-one differential-algebraic equations. Zbl 1419.49007
Martens, Björn; Gerdts, Matthias
2019
Lyapunov pairs in semilinear differential problems with state-dependent impulses. Zbl 1426.34074
Benedetti, I.; Cardinali, T.; Gabor, G.; Rubbioni, P.
2019
New constraint qualifications and optimality conditions for second order cone programs. Zbl 1423.90249
Zhang, Yi; Zhang, Liwei
2019
Regular and limiting normal cones to the graph of the subdifferential mapping of the nuclear norm. Zbl 1416.49018
Liu, Yulan; Pan, Shaohua
2019
The weak sequential closure of decomposable sets in Lebesgue spaces and its application to variational geometry. Zbl 1415.49014
Mehlitz, Patrick; Wachsmuth, Gerd
2019
Variations of deformations with self-contact on Lipschitz domains. Zbl 1431.35200
Palmer, Aaron Zeff
2019
Linearized M-stationarity conditions for general optimization problems. Zbl 1430.90556
Gfrerer, Helmut
2019
Correction to: Optimal control involving sweeping processes. Zbl 1453.49012
de Pinho, M. d. R.; Ferreira, M. M. A.; Smirnov, G. V.
2019
Pullback attractors for multivalued processes and application to nonautonomous problems with dynamic boundary conditions. Zbl 1473.35062
Samprogna, R. A.; Schiabel, K.; Gentile Moussa, C. B.
2019
On maximality of quasimonotone operators. Zbl 07058437
Bueno, Orestes; Cotrina, John
2019
Selective bi-coordinate method for limit non-smooth resource allocation type problems. Zbl 1420.90067
Konnov, I. V.
2019
Trajectories of differential inclusions on Riemannian manifolds and invariance. Zbl 1417.58007
2019
Infinite horizon problems in the calculus of variations. The role of transformations with an application to the brachistochrone problem. Zbl 1419.49018
Pickenhain, Sabine
2019
Existence and Lyapunov pairs for the perturbed sweeping process governed by a fixed set. Zbl 1432.34081
Vilches, Emilio
2019
Computation of the epsilon-subdifferential of convex piecewise linear-quadratic functions in optimal worst-case time. Zbl 07115099
Kumar, Deepak; Lucet, Yves
2019
Well-posedness and subdifferentials of optimal value and infimal convolution. Zbl 1430.49009
Ivanov, Grigorii E.; Thibault, Lionel
2019
A maximum principle for the controlled sweeping process. Zbl 1398.49015
Arroud, Chems Eddine; Colombo, Giovanni
2018
Generalized control systems in the space of probability measures. Zbl 1400.93330
Cavagnari, Giulia; Marigonda, Antonio; Nguyen, Khai T.; Priuli, Fabio S.
2018
About intrinsic transversality of pairs of sets. Zbl 1387.49023
Kruger, Alexander Y.
2018
Properties of chance constraints in infinite dimensions with an application to PDE constrained optimization. Zbl 1410.90135
Farshbaf-Shaker, M. H.; Henrion, R.; Hömberg, D.
2018
Perturbed evolution problems with continuous bounded variation in time and applications. Zbl 1403.34046
Azzam-Laouir, Dalila; Castaing, Charles; Monteiro Marques, M. D. P.
2018
(Sub-)differentiability of probability functions with elliptical distributions. Zbl 1416.90028
van Ackooij, W.; Aleksovska, I.; Munoz-Zuniga, M.
2018
On stochastic mirror-prox algorithms for stochastic Cartesian variational inequalities: randomized block coordinate and optimal averaging schemes. Zbl 07002699
Yousefian, Farzad; Nedić, Angelia; Shanbhag, Uday V.
2018
The limiting normal cone to pointwise defined sets in Lebesgue spaces. Zbl 1401.49018
Mehlitz, Patrick; Wachsmuth, Gerd
2018
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### Cited by 2,179 Authors

 31 Boţ, Radu Ioan 31 Mordukhovich, Boris S. 28 Kruger, Alexander Y. 26 Papageorgiou, Nikolaos S. 25 Yao, Jen-Chih 23 Bauschke, Heinz H. 22 Wang, Shawn Xianfu 22 Zaslavski, Alexander Yakovlevich 21 Csetnek, Ernö Robert 20 Soubeyran, Antoine 19 Hantoute, Abderrahim 18 Durea, Marius 18 López-Cerdá, Marco Antonio 18 Mehlitz, Patrick 18 Reich, Simeon 18 Ye, Jane J. 17 Adly, Samir 17 Combettes, Patrick L. 17 Pérez-Aros, Pedro 17 Van Ackooij, Wim 16 Noll, Dominikus 16 Zhang, Liwei 15 Arutyunov, Aram Vladimirovic 15 Gfrerer, Helmut 15 Kasyanov, Pavlo O. 14 Seeger, Alberto 14 Strugariu, Radu 14 Théra, Michel A. 14 Thibault, Lionel 14 Valero, José 13 Cánovas, María Josefa 13 Chuong, Thai Doan 13 Dang Van Hieu 13 Gasiński, Leszek 13 Goberna, Miguel Angel 13 Huynh Van Ngai 13 Kapustyan, Oleksiy V. 13 Parra, Juan 13 Wachsmuth, Gerd 13 Zeng, Shengda 12 Anh, Nguyen Le Hoang 12 Bounkhel, Messaoud 12 Nobakhtian, Soghra 12 Yao, Liangjin 11 Attouch, Hedy 11 Azzam-Laouir, Dalila 11 Beer, Gerald Alan 11 Borwein, Jonathan Michael 11 Correa, Rafael 11 Henrion, René 11 Martínez-Legaz, Juan-Enrique 11 Outrata, Jiří V. 11 Phan, Hung M. 11 Volle, Michel 11 Zhang, Jin 10 Castaing, Charles 10 Chen, Yanhong 10 Cibulka, Radek 10 da Cruz Neto, João Xavier 10 Dao, Minh Ngoc 10 Gorban, Nataliia V. 10 Hamel, Andreas H. 10 Izmailov, Alekseĭ F. 10 Kumam, Poom 10 Le, Ba Khiet 10 Li, Minghua 10 Luke, David Russell 10 Marigonda, Antonio 10 Motta, Monica 10 Movahedian, Nooshin 10 Nam, Nguyen Mau 10 Rudloff, Birgit 10 Tang, Yuchao 10 Thao, Nguyen Hieu 10 Vũ, Bằng Công 10 Winkert, Patrick 10 Zhang, Jie 9 Aragón Artacho, Francisco Javier 9 Burachik, Regina Sandra 9 Colombo, Giovanni 9 de Oliveira, Welington Luis 9 Hu, Yijun 9 Huang, Nan-Jing 9 Lindstrom, Scott B. 9 Nguyen Thi Toan 9 Penot, Jean-Paul 9 Phan Quôc Khánh 9 Pini, Rita 9 Royset, Johannes O. 9 Sun, Xiangkai 9 Tam, Matthew K. 9 Wen, Chingfeng 9 Yang, Xiaoqi 8 Ansari, Qamrul Hasan 8 Apkarian, Pierre 8 Bello Cruz, Jose Yunier 8 Bianchi, Monica 8 Bui, Hoa T. 8 Cuong, Nguyen Duy 8 Flåm, Sjur Didrik ...and 2,079 more Authors
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### Cited in 300 Journals

 175 Journal of Optimization Theory and Applications 175 Set-Valued and Variational Analysis 131 Optimization 92 SIAM Journal on Optimization 73 Journal of Mathematical Analysis and Applications 73 Mathematical Programming. Series A. Series B 64 Optimization Letters 56 Journal of Global Optimization 48 Computational Optimization and Applications 43 Positivity 41 SIAM Journal on Control and Optimization 36 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 36 Journal of Convex Analysis 31 Vietnam Journal of Mathematics 29 Numerical Functional Analysis and Optimization 27 Journal of Inequalities and Applications 26 Applied Mathematics and Optimization 24 Journal of Differential Equations 24 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 22 Journal of Fixed Point Theory and Applications 21 Annals of Operations Research 20 Applicable Analysis 16 Numerical Algorithms 16 SIAM Journal on Imaging Sciences 15 Discrete and Continuous Dynamical Systems. Series B 15 Fixed Point Theory and Applications 14 Optimization Methods & Software 13 Mathematics of Operations Research 13 Journal of Nonlinear and Variational Analysis 12 Applied Mathematics and Computation 12 Topology and its Applications 12 Discrete and Continuous Dynamical Systems. Series S 11 Results in Mathematics 11 Operations Research Letters 11 Journal of Mathematical Imaging and Vision 11 Mathematical Problems in Engineering 11 Mediterranean Journal of Mathematics 11 Journal of Industrial and Management Optimization 10 Journal of Scientific Computing 10 Calculus of Variations and Partial Differential Equations 10 Computational and Applied Mathematics 10 Filomat 9 European Journal of Operational Research 9 Journal of Mathematical Sciences (New York) 9 Discrete and Continuous Dynamical Systems 9 Abstract and Applied Analysis 8 Journal of the Operations Research Society of China 8 Journal of Function Spaces 7 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Topological Methods in Nonlinear Analysis 7 Top 7 Mathematical Methods of Operations Research 7 Journal of the Australian Mathematical Society 7 Advances in Difference Equations 7 Journal of Nonlinear Science and Applications 7 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 7 Evolution Equations and Control Theory 6 Inverse Problems 6 Proceedings of the American Mathematical Society 6 Linear Algebra and its Applications 6 Applied and Computational Harmonic Analysis 6 Optimization and Engineering 6 Boundary Value Problems 5 Journal of Computational and Applied Mathematics 5 Journal of Mathematical Economics 5 Rendiconti del Circolo Matemàtico di Palermo. Serie II 5 Asia-Pacific Journal of Operational Research 5 SIAM Journal on Scientific Computing 5 Advances in Computational Mathematics 5 Communications in Contemporary Mathematics 5 Nonlinear Analysis. Real World Applications 5 Acta Mathematica Scientia. Series B. (English Edition) 5 Thai Journal of Mathematics 5 Numerical Algebra, Control and Optimization 5 Mathematical Control and Related Fields 5 Fixed Point Theory and Algorithms for Sciences and Engineering 4 Mathematical Methods in the Applied Sciences 4 Beiträge zur Algebra und Geometrie 4 Automatica 4 Journal of Functional Analysis 4 Transactions of the American Mathematical Society 4 Acta Applicandae Mathematicae 4 SIAM Journal on Mathematical Analysis 4 Finance and Stochastics 4 International Journal of Theoretical and Applied Finance 4 Journal of Dynamical and Control Systems 4 Differential Equations 4 Foundations of Computational Mathematics 4 Communications on Pure and Applied Analysis 4 Symmetry 4 SIAM Journal on Mathematics of Data Science 4 OJMO. Open Journal of Mathematical Optimization 3 International Journal of Control 3 Acta Mathematica Vietnamica 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Systems & Control Letters 3 MCSS. Mathematics of Control, Signals, and Systems 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Electronic Journal of Differential Equations (EJDE) 3 Economic Theory ...and 200 more Journals
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### Cited in 49 Fields

 1,065 Operations research, mathematical programming (90-XX) 929 Calculus of variations and optimal control; optimization (49-XX) 514 Operator theory (47-XX) 380 Numerical analysis (65-XX) 199 Partial differential equations (35-XX) 179 Ordinary differential equations (34-XX) 151 General topology (54-XX) 134 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 129 Functional analysis (46-XX) 106 Real functions (26-XX) 101 Global analysis, analysis on manifolds (58-XX) 81 Systems theory; control (93-XX) 71 Dynamical systems and ergodic theory (37-XX) 65 Convex and discrete geometry (52-XX) 60 Computer science (68-XX) 55 Information and communication theory, circuits (94-XX) 50 Measure and integration (28-XX) 31 Statistics (62-XX) 27 Mechanics of deformable solids (74-XX) 24 Probability theory and stochastic processes (60-XX) 22 Biology and other natural sciences (92-XX) 21 Approximations and expansions (41-XX) 14 Linear and multilinear algebra; matrix theory (15-XX) 13 Difference and functional equations (39-XX) 13 Fluid mechanics (76-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 9 Differential geometry (53-XX) 8 Algebraic topology (55-XX) 8 Mechanics of particles and systems (70-XX) 7 General and overarching topics; collections (00-XX) 7 Mathematical logic and foundations (03-XX) 7 Geometry (51-XX) 7 Classical thermodynamics, heat transfer (80-XX) 6 Integral equations (45-XX) 5 Nonassociative rings and algebras (17-XX) 5 Optics, electromagnetic theory (78-XX) 4 History and biography (01-XX) 3 Combinatorics (05-XX) 3 Algebraic geometry (14-XX) 3 Topological groups, Lie groups (22-XX) 2 Category theory; homological algebra (18-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Quantum theory (81-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Geophysics (86-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Group theory and generalizations (20-XX) 1 Functions of a complex variable (30-XX) 1 Manifolds and cell complexes (57-XX)