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## Rockafellar, Ralph Tyrrell

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 Author ID: rockafellar.ralph-tyrrell Published as: Rockafellar, R.; Rockafellar, R. T.; Rockafellar, R. Terry; Rockafellar, R. Tyrrell; Rockafellar, Ralph Tyrrell; Rockafellar, Terry; Rockafellar, Tyrrell; Rockafellar, Tyrrell R. Homepage: https://sites.math.washington.edu/~rtr/mypage.html External Links: MGP · Wikidata · GND
 Documents Indexed: 230 Publications since 1964, including 13 Books Biographic References: 4 Publications
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#### Co-Authors

 124 single-authored 27 Wets, Roger Jean-Baptiste 15 Dontchev, Asen L. 11 Poliquin, René A. 5 Jofré, Alejandro 5 Levy, Adam B. 5 Uryasev, Stan 4 Loewen, Philip D. 4 Royset, Johannes O. 3 Goebel, Rafal 3 King, Alan J. 3 Lau, Anthony To-Ming 3 Mordukhovich, Boris S. 3 Sun, Jie 3 Takahashi, Wataru 3 Tanaka, Tamaki 3 Théra, Michel A. 3 Zabarankin, Michael 2 Dermody, James Cuevas 2 Hoàng Xuân Phù 2 Huynh Van Ngai 2 Maisonneuve, Olivier 2 Patriksson, Michael 2 Wolenski, Peter R. 2 Xu, Hong-Kun 1 Alart, Pierre 1 Asplund, Edgar 1 Beer, Gerald Alan 1 Benavides, T. D. 1 Brøndsted, Arne 1 Chen, George H-G. 1 Eberhard, Andrew S. 1 Eve, R. A. 1 Gale, David 1 Ioffe, Alexander Davidovich 1 Kim, Do Sang 1 Klee, Victor LaRue 1 Krastanov, Mikhail Ivanov 1 Kripke, Bernard R. 1 Lewis, Adrian S. 1 Llorens-Fuster, Enrique 1 López Acedo, Genaro 1 Miranda, S. I. 1 Nghia, Tran T. A. 1 Pennanen, Teemu 1 Reddy, B. Dayanand 1 Sarabi, M. Ebrahim 1 Somlyódy, László 1 Spingarn, Jonathan E. 1 Thibault, Lionel 1 Tsyurmasto, Peter 1 Uryasev, Stanislav P. 1 Valadier, Michel 1 Veliov, Vladimir M. 1 Veremyev, Alexander 1 Nguyen Dong Yen 1 Zagrodny, Dariusz 1 Zhu, Ciyou
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#### Serials

 13 SIAM Journal on Control and Optimization 12 Transactions of the American Mathematical Society 12 Mathematical Programming. Series A. Series B 10 SIAM Journal on Optimization 9 Mathematics of Operations Research 9 Pacific Journal of Mathematics 5 Journal of Mathematical Analysis and Applications 5 Journal of Convex Analysis 5 Journal of Nonlinear and Convex Analysis 5 Nonlinear Analysis. Theory, Methods & Applications 4 Journal of Optimization Theory and Applications 4 Proceedings of the American Mathematical Society 4 Set-Valued Analysis 4 Vietnam Journal of Mathematics 3 Canadian Journal of Mathematics 3 Mathematical Programming Study 3 Set-Valued and Variational Analysis 2 Stochastics 2 Control and Cybernetics 2 Duke Mathematical Journal 2 Journal of Economic Theory 2 Mathematical Programming 2 Mathematica Scandinavica 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Annals of Operations Research 2 Mathematical Finance 2 Bulletin of the American Mathematical Society 2 SIAM Journal on Control 1 Advances in Mathematics 1 Journal of Computational and Applied Mathematics 1 Journal of Mathematical Economics 1 Mathematische Annalen 1 The Mathematics Student 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Proceedings of the London Mathematical Society. Third Series 1 Quarterly of Applied Mathematics 1 Applied Stochastic Models and Data Analysis 1 Transportation Science 1 Journal of Global Optimization 1 European Journal of Operational Research 1 SIAM Review 1 Computational Optimization and Applications 1 Calculus of Variations and Partial Differential Equations 1 Economic Theory 1 Finance and Stochastics 1 Computational Management Science 1 Journal of Mathematics and Mechanics 1 Journal of the Society for Industrial & Applied Mathematics 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 Grundlehren der Mathematischen Wissenschaften 1 Advances in Mechanics and Mathematics 1 Applied and Computational Mathematics 1 Matapli 1 Springer Monographs in Mathematics 1 Springer Series in Operations Research and Financial Engineering 1 Research and Education in Mathematics
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#### Fields

 142 Operations research, mathematical programming (90-XX) 123 Calculus of variations and optimal control; optimization (49-XX) 23 Real functions (26-XX) 23 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 19 Operator theory (47-XX) 17 Global analysis, analysis on manifolds (58-XX) 15 Systems theory; control (93-XX) 14 Numerical analysis (65-XX) 7 Functional analysis (46-XX) 7 Convex and discrete geometry (52-XX) 6 General and overarching topics; collections (00-XX) 6 Measure and integration (28-XX) 6 General topology (54-XX) 3 History and biography (01-XX) 2 Ordinary differential equations (34-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Approximations and expansions (41-XX) 2 Probability theory and stochastic processes (60-XX) 2 Mechanics of deformable solids (74-XX) 1 Combinatorics (05-XX) 1 Partial differential equations (35-XX) 1 Statistics (62-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH

208 Publications have been cited 19,156 times in 12,549 Documents Cited by Year
Convex analysis. Zbl 0193.18401
Rockafellar, R. Tyrrell
1970
Variational analysis. Zbl 0888.49001
Rockafellar, R. Tyrrell; Wets, Roger J.-B.
1998
Monotone operators and the proximal point algorithm. Zbl 0358.90053
Rockafellar, R. Tyrrell
1976
Conjugate convex functions in nonlinear programming. Zbl 0229.90020
Rockafellar, R. T.
1970
Convex analysis. Zbl 0932.90001
Rockafellar, R. Tyrrell
1997
Convex functions, monotone operators and variational inequalities. Zbl 0202.14303
Rockafellar, R. T.
1970
On the maximality of sums of nonlinear monotone operators. Zbl 0222.47017
Rockafellar, R. T.
1970
Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Zbl 0402.90076
Rockafellar, R. T.
1976
State constraints in convex control problems of Bolza. Zbl 0224.49003
Rockafellar, R. T.
1972
Conjugate duality and optimization. Zbl 0296.90036
Rockafellar, R. Tyrrell
1974
On the maximal monotonicity of subdifferential mappings. Zbl 0199.47101
Rockafellar, R. T.
1970
Implicit functions and solution mappings. A view from variational analysis. Zbl 1178.26001
Dontchev, Asen L.; Rockafellar, R. Tyrrell
2009
Scenarios and policy aggregation in optimization under uncertainty. Zbl 0729.90067
Rockafellar, R. T.; Wets, Roger J.-B.
1991
Generalized directional derivatives and subgradients of nonconvex functions. Zbl 0447.49009
Rockafellar, R. T.
1980
Local differentiability of distance functions. Zbl 0960.49018
Poliquin, R. A.; Rockafellar, R. T.; Thibault, L.
2000
Characterization of the subdifferentials of convex functions. Zbl 0145.15901
Rockafellar, R. T.
1966
Integrals which are convex functionals. Zbl 0159.43804
Rockafellar, R. T.
1968
Network flows and monotropic optimization. Zbl 0596.90055
Rockafellar, R. T.
1984
Generalized deviations in risk analysis. Zbl 1150.90006
Rockafellar, R. Tyrrell; Uryasev, Stan; Zabarankin, Michael
2006
The theory of subgradients and its applications to problems of optimization. Convex and nonconvex functions. Zbl 0462.90052
Rockafellar, R. T.
1981
Characterizations of strong regularity for variational inequalities over polyhedral convex sets. Zbl 0899.49004
Dontchev, A. L.; Rockafellar, R. T.
1996
Directionally Lipschitzian functions and subdifferential calculus. Zbl 0413.49015
Rockafellar, R. T.
1979
Integrals which are convex functionals. II. Zbl 0236.46031
Rockafellar, R. T.
1971
On the subdifferentiability of convex functions. Zbl 0141.11801
Brøndsted, Arne; Rockafellar, R. T.
1965
Augmented Lagrange multiplier functions and duality in nonconvex programming. Zbl 0257.90046
Rockafellar, R. Tyrrell
1974
Convex functions and duality in optimization problems and dynamics. Zbl 0186.23901
Rockafellar, R. T.
1969
The multiplier method of Hestenes and Powell applied to convex programming. Zbl 0254.90045
Rockafellar, R. T.
1973
Clarke’s tangent cones and the boundaries of closed sets in $$\mathbb{R}^n$$. Zbl 0443.26010
Rockafellar, R. T.
1979
Integral functionals, normal integrands and measurable selections. Zbl 0374.49001
Rockafellar, Tyrrell
1976
Prox-regular functions in variational analysis. Zbl 0861.49015
Poliquin, R. A.; Rockafellar, R. T.
1996
Lagrange multipliers and optimality. Zbl 0779.49024
Rockafellar, R. Tyrrell
1993
Lipschitzian properties of multifunctions. Zbl 0573.54011
Rockafellar, R. Tyrrell
1985
Duality and stability in extremum problems involving convex functions. Zbl 0154.44902
Rockafellar, R. T.
1967
A dual approach to solving nonlinear programming problems by unconstrained optimization. Zbl 0279.90035
Rockafellar, R. Tyrrell
1973
Implicit functions and solution mappings. A view from variational analysis. 2nd updated ed. Zbl 1337.26003
Dontchev, Asen L.; Rockafellar, R. Tyrrell
2014
Regularity and conditioning of solution mappings in variational analysis. Zbl 1046.49021
Dontchev, A. L.; Rockafellar, R. T.
2004
Local boundedness of nonlinear, monotone operators. Zbl 0175.45002
Rockafellar, R. T.
1969
The radius of metric regularity. Zbl 1042.49026
Dontchev, A. L.; Lewis, A. S.; Rockafellar, R. T.
2003
First- and second-order epi-differentiability in nonlinear programming. Zbl 0655.49010
Rockafellar, R. T.
1988
Extension of Fenchel’s duality theorem for convex functions. Zbl 0138.09301
Rockafellar, R. T.
1966
Measurable dependence of convex sets and functions on parameters. Zbl 0202.33804
Rockafellar, R. T.
1969
Conjugate convex functions in optimal control and the calculus of variations. Zbl 0218.49004
Rockafellar, R. T.
1970
Proto-differentiability of set-valued mappings and its applications in optimization. Zbl 0674.90082
Rockafellar, R. T.
1989
Tilt stability of a local minimum. Zbl 0918.49016
Poliquin, R. A.; Rockafellar, R. T.
1998
Gradients of convex functions. Zbl 0181.41901
Asplund, E.; Rockafellar, R. T.
1969
Level sets and continuity of conjugate convex functions. Zbl 0145.15802
Rockafellar, R. T.
1966
Convergence rates in forward–backward splitting. Zbl 0876.49009
Chen, George H-G.; Rockafellar, R. T.
1997
Equivalent subgradient versions of Hamiltonian and Euler-Lagrange equations in variational analysis. Zbl 0878.49012
Rockafellar, R. Tyrrell
1996
Saddle-points and convex analysis. Zbl 0242.90044
Rockafellar, Tyrrell
1971
Second-order optimality conditions in nonlinear programming obtained by way of epi-derivatives. Zbl 0698.90070
Rockafellar, R. Tyrrell
1989
Saddle points of Hamiltonian systems in convex Lagrange problems having a nonzero discount rate. Zbl 0333.90007
Rockafellar, R. Tyrrell
1976
Optimality conditions in portfolio analysis with general deviation measures. Zbl 1138.91474
Rockafellar, R. Tyrrell; Uryasev, Stan; Zabarankin, Michael
2006
Proximal subgradients, marginal values, and augmented Lagrangians in nonconvex optimization. Zbl 0492.90073
Rockafellar, R. T.
1981
Second-order subdifferential calculus with applications to tilt stability in optimization. Zbl 1260.49022
Mordukhovich, B. S.; Rockafellar, R. T.
2012
Extensions of subgradient calculus with applications to optimization. Zbl 0593.49013
Rockafellar, R. T.
1985
Stability of locally optimal solutions. Zbl 0965.49018
Levy, A. B.; Poliquin, R. A.; Rockafellar, R. T.
2000
Existence theorems for general control problems of Bolza and Lagrange. Zbl 0319.49001
Rockafellar, Tyrrell R.
1975
Monotone processes of convex and concave type. Zbl 0189.19602
Rockafellar, R. Tyrrell
1967
Convex integral functionals and duality. Zbl 0326.49008
Rockafellar, R. T.
1974
Asymptotic theory for solutions in statistical estimation and stochastic programming. Zbl 0798.90115
King, Alan J.; Rockafellar, Tyrrell
1993
Lagrange multipliers and subderivatives of optimal value functions in nonlinear programming. Zbl 0478.90060
Rockafellar, R. T.
1982
Robinson’s implicit function theorem and its extensions. Zbl 1172.49013
Dontchev, A. L.; Rockafellar, R. T.
2009
Existence and duality theorems for convex problems of Bolza. Zbl 0255.49007
Rockafellar, R. T.
1971
Sensitivity analysis for nonsmooth generalized equations. Zbl 0766.90075
King, Alan J.; Rockafellar, R. Tyrrell
1992
Convex analysis. (Vypuklyi analiz.) Übersetzung aus dem Englischen von A. D. Ioffe und V. M. Tihomirov. Zbl 0251.90035
Rockafellar, R. Tyrrell
1973
A Lagrangian finite generation technique for solving linear-quadratic problems in stochastic programming. Zbl 0599.90090
Rockafellar, R. T.; Wets, R. J.-B.
1986
Favorable classes of Lipschitz-continuous functions in subgradient optimization. Zbl 0511.26009
Rockafellar, R. Tyrrell
1982
Optimal control of unbounded differential inclusions. Zbl 0823.49016
Loewen, Philip D.; Rockafellar, R. T.
1994
Maximal monotone relations and the second derivatives of nonsmooth functions. Zbl 0581.49009
Rockafellar, R. T.
1985
Directional differentiability of the optimal value function in a nonlinear programming problem. Zbl 0546.90088
Rockafellar, R. T.
1984
Saddle points of Hamiltonian systems in convex problems of Lagrange. Zbl 0248.49016
Rockafellar, R. T.
1973
Generalized linear-quadratic problems of deterministic and stochastic optimal control in discrete time. Zbl 0714.49036
Rockafellar, R. T.; Wets, R. J.-B.
1990
A derivative-coderivative inclusion in second-order nonsmooth analysis. Zbl 0897.49014
Rockafellar, R. T.; Zagrodny, D.
1997
Variational inequalities and economic equilibrium. Zbl 1276.91070
Jofré, Alejandro; Rockafellar, R. Terry; Wets, Roger J.-B.
2007
Linear-quadratic programming and optimal control. Zbl 0617.49010
Rockafellar, R. T.
1987
Characterizations of full stability in constrained optimization. Zbl 1284.49032
Mordukhovich, B. S.; Rockafellar, R. T.; Sarabi, M. E.
2013
The optimal recourse problem in discrete time: $$L^1$$-multipliers for inequality constraints. Zbl 0397.90078
Rockafellar, R. T.; Wets, R. J-B.
1978
Stochastic convex programming: Relatively complete recourse and induced feasibility. Zbl 0346.90058
Rockafellar, R. T.; Wets, R. J.-B.
1976
Some convex programs whose duals are linearly constrained. Zbl 0252.90046
Rockafellar, R. Tyrrell
1970
A general correspondence between dual minimax problems and convex programs. Zbl 0162.23103
Rockafellar, R. T.
1968
Generalized second derivatives of convex functions and saddle functions. Zbl 0712.49011
Rockafellar, R. T.
1990
Computational schemes for large-scale problems in extended linear- quadratic programming. Zbl 0735.90050
Rockafellar, R. T.
1990
Generalized Hamiltonian equations for convex problems of Lagrange. Zbl 0199.43002
Rockafellar, R. T.
1970
Convex integral functionals and duality. Zbl 0295.49006
Rockafellar, R. Tyrrell
1971
Sensitivity analysis of solutions to generalized equations. Zbl 0815.47077
Levy, A. B.; Rockafellar, R. T.
1994
Stochastic variational inequalities: single-stage to multistage. Zbl 1378.49010
Rockafellar, R. Tyrrell; Wets, Roger J-B
2017
Second derivatives in convex analysis. Zbl 1003.49017
Rockafellar, R. T.
1999
Conditional value-at-risk: optimization approach. Zbl 0989.91052
Uryasev, Stanislav; Rockafellar, R. Tyrrell
2001
The Euler and Weierstrass conditions for nonsmooth variational problems. Zbl 0838.49015
Ioffe, A. D.; Rockafellar, R. T.
1996
On the interchange of subdifferentiation and conditional expectation for convex functionals. Zbl 0487.49006
Rockafellar, R. T.; Wets, R. J. B.
1982
Stochastic convex programming: basic duality. Zbl 0339.90048
Rockafellar, R. T.; Wets, R. J.-B.
1976
On the virtual convexity of the domain and range of a nonlinear maximal monotone operator. Zbl 0181.42202
Rockafellar, R. T.
1970
Full stability in finite-dimensional optimization. Zbl 1308.90126
Mordukhovich, B. S.; Nghia, T. T. A.; Rockafellar, R. T.
2015
Generalized Hessian properties of regularized nonsmooth functions. Zbl 0863.49010
Poliquin, R. A.; Rockafellar, R. T.
1996
An internal variable theory of elastoplasticity based on the maximum plastic work inequality. Zbl 0693.73008
Eve, R. A.; Reddy, B. D.; Rockafellar, R. T.
1990
La théorie des sous-gradients et ses applications à l’optimisation. Fonctions convexes et non convexes. Zbl 0421.90045
Rockafellar, R. Tyrrell
1979
Nonanticipativity and $$\mathcal L^1$$-martingales in stochastic optimization problems. Zbl 0377.90073
Rockafellar, R. T.; Wets, R. J.-B.
1976
Newton’s method for generalized equations: a sequential implicit function theorem. Zbl 1190.49024
Dontchev, A. L.; Rockafellar, R. T.
2010
Convex functions on convex polytopes. Zbl 0246.26009
Gale, David; Klee, Victor; Rockafellar, R. T.
1968
A characterization of epi-convergence in terms of convergence of level sets. Zbl 0769.49011
Beer, Gerald; Rockafellar, R. T.; Wets, Roger J.-B.
1992
Solving Lagrangian variational inequalities with applications to stochastic programming. Zbl 1445.90069
Rockafellar, R. Tyrrell; Sun, Jie
2020
Solving monotone stochastic variational inequalities and complementarity problems by progressive hedging. Zbl 1421.90100
Rockafellar, R. Tyrrell; Sun, Jie
2019
Variational convexity and the local monotonicity of subgradient mappings. Zbl 1428.49021
Rockafellar, R. Tyrrell
2019
Progressive decoupling of linkages in optimization and variational inequalities with elicitable convexity or monotonicity. Zbl 07146007
Rockafellar, R. Tyrrell
2019
Superquantile/CVaR risk measures: second-order theory. Zbl 1391.91163
Rockafellar, R. Tyrrell; Royset, Johannes O.
2018
Solving stochastic programming problems with risk measures by progressive hedging. Zbl 1416.90027
Rockafellar, R. Tyrrell
2018
Variational analysis of Nash equilibrium. Zbl 1407.91022
Rockafellar, R. Tyrrell
2018
Stochastic variational inequalities: single-stage to multistage. Zbl 1378.49010
Rockafellar, R. Tyrrell; Wets, Roger J-B
2017
General economic equilibrium with financial markets and retainability. Zbl 1405.91742
Jofré, A.; Rockafellar, R. T.; Wets, R. J-B.
2017
Full stability in finite-dimensional optimization. Zbl 1308.90126
Mordukhovich, B. S.; Nghia, T. T. A.; Rockafellar, R. T.
2015
Measures of residual risk with connections to regression, risk tracking, surrogate models, and ambiguity. Zbl 1316.91016
Rockafellar, R. Tyrrell; Royset, Johannes O.
2015
Implicit functions and solution mappings. A view from variational analysis. 2nd updated ed. Zbl 1337.26003
Dontchev, Asen L.; Rockafellar, R. Tyrrell
2014
Random variables, monotone relations, and convex analysis. Zbl 1330.60009
Rockafellar, R. T.; Royset, J. O.
2014
Superquantile regression with applications to buffered reliability, uncertainty quantification, and conditional value-at-risk. Zbl 1305.62175
Rockafellar, R. T.; Royset, J. O.; Miranda, S. I.
2014
Convex analysis and financial equilibrium. Zbl 1309.91086
Jofré, A.; Rockafellar, R. T.; Wets, R. J.-B.
2014
Characterizations of full stability in constrained optimization. Zbl 1284.49032
Mordukhovich, B. S.; Rockafellar, R. T.; Sarabi, M. E.
2013
Convergence of inexact Newton methods for generalized equations. Zbl 1272.49047
Dontchev, A. L.; Rockafellar, R. T.
2013
An Euler-Newton continuation method for tracking solution trajectories of parametric variational inequalities. Zbl 1272.49012
Dontchev, A. L.; Krastanov, M. I.; Rockafellar, R. T.; Veliov, V. M.
2013
Second-order subdifferential calculus with applications to tilt stability in optimization. Zbl 1260.49022
Mordukhovich, B. S.; Rockafellar, R. T.
2012
Parametric stability of solutions in models of economic equilibrium. Zbl 1256.49021
Dontchev, Asen L.; Rockafellar, Ralph Tyrrell
2012
A time-embedded approach to economic equilibrium with incomplete financial markets. Zbl 1216.91041
Jofré, A.; Rockafellar, R. T.; Wets, R. J.-B.
2011
Newton’s method for generalized equations: a sequential implicit function theorem. Zbl 1190.49024
Dontchev, A. L.; Rockafellar, R. T.
2010
A calculus of prox-regularity. Zbl 1194.49049
Poliquin, R. A.; Rockafellar, R. T.
2010
Implicit functions and solution mappings. A view from variational analysis. Zbl 1178.26001
Dontchev, Asen L.; Rockafellar, R. Tyrrell
2009
Robinson’s implicit function theorem and its extensions. Zbl 1172.49013
Dontchev, A. L.; Rockafellar, R. T.
2009
Hamiltonian trajectories and saddle points in mathematical economics. Zbl 1235.91131
Rockafellar, R.
2009
Risk tuning with generalized linear regression. Zbl 1218.90158
Rockafellar, R. Tyrrell; Uryasev, Stan; Zabarankin, Michael
2008
Local strong convexity and local Lipschitz continuity of the gradient of convex functions. Zbl 1149.26022
Goebel, Rafal; Rockafellar, Ralph Tyrrell
2008
Linear-convex control and duality. Zbl 1206.49036
Rockafellar, R. T.; Goebel, R.
2008
Variational inequalities and economic equilibrium. Zbl 1276.91070
Jofré, Alejandro; Rockafellar, R. Terry; Wets, Roger J.-B.
2007
Generalized deviations in risk analysis. Zbl 1150.90006
Rockafellar, R. Tyrrell; Uryasev, Stan; Zabarankin, Michael
2006
Optimality conditions in portfolio analysis with general deviation measures. Zbl 1138.91474
Rockafellar, R. Tyrrell; Uryasev, Stan; Zabarankin, Michael
2006
Nonsmooth mechanics and analysis. Theoretical and numerical advances. Zbl 1110.74006
Alart, P. (ed.); Maisonneuve, O. (ed.); Rockafellar, R. T. (ed.)
2006
A variational inequality scheme for determining an economic equilibrium of classical or extended type. Zbl 1113.49013
Jofre, A.; Rockafellar, R. T.; Wets, R. J.-B.
2005
Regularity and conditioning of solution mappings in variational analysis. Zbl 1046.49021
Dontchev, A. L.; Rockafellar, R. T.
2004
Hamilton-Jacobi theory and parametric analysis in fully convex problems of optimal control. Zbl 1083.49022
Rockafellar, R. Tyrrell
2004
The radius of metric regularity. Zbl 1042.49026
Dontchev, A. L.; Lewis, A. S.; Rockafellar, R. T.
2003
A property of piecewise smooth functions. Zbl 1042.90045
Rockafellar, R. T.
2003
A mathematical model and descent algorithm for bilevel traffic management. Zbl 1134.90319
Patriksson, Michael; Rockafellar, R. Tyrrell
2002
Generalized conjugacy in Hamilton-Jacobi theory for fully convex Lagrangians. Zbl 1023.49023
Goebel, Rafal; Rockafellar, R. T.
2002
Graphical convergence of sums of monotone mappings. Zbl 1010.47031
Pennanen, T.; Rockafellar, R. T.; Théra, M.
2002
Conditional value-at-risk: optimization approach. Zbl 0989.91052
Uryasev, Stanislav; Rockafellar, R. Tyrrell
2001
Ample parameterization of variational inclusions. Zbl 1008.49009
Dontchev, A. L.; Rockafellar, R. T.
2001
Convex analysis in the calculus of variations. Zbl 1011.49013
Rockafellar, R. T.
2001
Primal-dual solution perturbations in convex optimization. Zbl 0984.90043
Dontchev, A. L.; Rockafellar, R. T.
2001
Local differentiability of distance functions. Zbl 0960.49018
Poliquin, R. A.; Rockafellar, R. T.; Thibault, L.
2000
Stability of locally optimal solutions. Zbl 0965.49018
Levy, A. B.; Poliquin, R. A.; Rockafellar, R. T.
2000
Convexity in Hamilton–Jacobi theory. I: Dynamics and duality. Zbl 0998.49018
Rockafellar, R. Tyrrell; Wolenski, Peter R.
2000
Convexity in Hamilton–Jacobi theory. II: Envelope representations. Zbl 0998.49019
Rockafellar, R. Tyrrell; Wolenski, Peter R.
2000
Second-order convex analysis. Zbl 0960.49017
Rockafellar, R. Tyrrell
2000
Extended nonlinear programming. Zbl 0986.90057
Rockafellar, R. Tyrrell
2000
Second derivatives in convex analysis. Zbl 1003.49017
Rockafellar, R. T.
1999
Duality and optimality in multistage stochastic programming. Zbl 0920.90113
Rockafellar, R. T.
1999
Variational analysis. Zbl 0888.49001
Rockafellar, R. Tyrrell; Wets, Roger J.-B.
1998
Tilt stability of a local minimum. Zbl 0918.49016
Poliquin, R. A.; Rockafellar, R. T.
1998
Convex analysis. Zbl 0932.90001
Rockafellar, R. Tyrrell
1997
Convergence rates in forward–backward splitting. Zbl 0876.49009
Chen, George H-G.; Rockafellar, R. T.
1997
A derivative-coderivative inclusion in second-order nonsmooth analysis. Zbl 0897.49014
Rockafellar, R. T.; Zagrodny, D.
1997
Bolza problems with general time constraints. Zbl 0904.49014
Loewen, P. D.; Rockafellar, R. T.
1997
Characterizations of Lipschitzian stability in nonlinear programming. Zbl 0891.90146
Dontchev, A. L.; Rockafellar, R. T.
1997
Characterizations of strong regularity for variational inequalities over polyhedral convex sets. Zbl 0899.49004
Dontchev, A. L.; Rockafellar, R. T.
1996
Prox-regular functions in variational analysis. Zbl 0861.49015
Poliquin, R. A.; Rockafellar, R. T.
1996
Equivalent subgradient versions of Hamiltonian and Euler-Lagrange equations in variational analysis. Zbl 0878.49012
Rockafellar, R. Tyrrell
1996
The Euler and Weierstrass conditions for nonsmooth variational problems. Zbl 0838.49015
Ioffe, A. D.; Rockafellar, R. T.
1996
Generalized Hessian properties of regularized nonsmooth functions. Zbl 0863.49010
Poliquin, R. A.; Rockafellar, R. T.
1996
New necessary conditions for the generalized problem of Bolza. Zbl 0871.49023
Loewen, P. D.; Rockafellar, R. T.
1996
Variational conditions and the proto-differentiation of partial subgradient mappings. Zbl 0858.49014
Levy, A. B.; Rockafellar, R. T.
1996
Second-order nonsmooth analysis in nonlinear programming. Zbl 0939.90022
Poliquin, René; Rockafellar, Terry
1995
Tax basis and nonlinearity in cash stream valuation. Zbl 0866.90013
Dermody, Jaime Cuevas; Rockafellar, R. Tyrrell
1995
Sensitivity of solutions in nonlinear programming problems with nonunique multipliers. Zbl 0945.90066
Levy, A. B.; Rockafellar, R. T.
1995
Monotone relations and network equilibrium. Zbl 0847.49012
Rockafellar, R. Tyrrell
1995
Optimal control of unbounded differential inclusions. Zbl 0823.49016
Loewen, Philip D.; Rockafellar, R. T.
1994
Sensitivity analysis of solutions to generalized equations. Zbl 0815.47077
Levy, A. B.; Rockafellar, R. T.
1994
Proto-derivative formulas for basic subgradient mappings in mathematical programming. Zbl 0813.49019
Poliquin, R. A.; Rockafellar, R. T.
1994
A finite simplex-active-set method for monotropic piecewise quadratic programming. Zbl 0828.90102
Rockafellar, R. T.; Sun, J.
1994
Lagrange multipliers and optimality. Zbl 0779.49024
Rockafellar, R. Tyrrell
1993
Asymptotic theory for solutions in statistical estimation and stochastic programming. Zbl 0798.90115
King, Alan J.; Rockafellar, Tyrrell
1993
Zhu, Ciyou; Rockafellar, R. T.
1993
A calculus of epi-derivatives applicable to optimization. Zbl 0803.90113
Poliquin, R. A.; Rockafellar, R. T.
1993
Subgradients and variational analysis. Zbl 0889.49011
Rockafellar, R. T.
1993
Dualization of subgradient conditions for optimality. Zbl 0786.49012
Rockafellar, R. T.
1993
Sensitivity analysis for nonsmooth generalized equations. Zbl 0766.90075
King, Alan J.; Rockafellar, R. Tyrrell
1992
A characterization of epi-convergence in terms of convergence of level sets. Zbl 0769.49011
Beer, Gerald; Rockafellar, R. T.; Wets, Roger J.-B.
1992
Amenable functions in optimization. Zbl 1050.49513
Poliquin, R. A.; Rockafellar, R. T.
1992
A dual strategy for the implementation of the aggregation principle in decision making under uncertainty. Zbl 0800.90002
Rockafellar, R. T.; Wets, Roger J.-B.
1992
Cosmic convergence. Zbl 0793.49007
Rockafellar, R. T.; Wets, R. J.-B.
1992
Scenarios and policy aggregation in optimization under uncertainty. Zbl 0729.90067
Rockafellar, R. T.; Wets, Roger J.-B.
1991
The adjoint arc in nonsmooth optimization. Zbl 0734.49009
Loewen, Philip D.; Rockafellar, R. T.
1991
Cash stream valuation in the face of transaction costs and taxes. Zbl 0900.90110
Dermody, Jaime Cuevas; Rockafellar, R. Tyrrell
1991
Large-scale extended linear-quadratic programming and multistage optimization. Zbl 0743.90086
Rockafellar, R. T.
1991
On a special class of convex functions. Zbl 0795.49015
Rockafellar, R. T.
1991
Generalized linear-quadratic problems of deterministic and stochastic optimal control in discrete time. Zbl 0714.49036
Rockafellar, R. T.; Wets, R. J.-B.
1990
Generalized second derivatives of convex functions and saddle functions. Zbl 0712.49011
Rockafellar, R. T.
1990
Computational schemes for large-scale problems in extended linear- quadratic programming. Zbl 0735.90050
Rockafellar, R. T.
1990
An internal variable theory of elastoplasticity based on the maximum plastic work inequality. Zbl 0693.73008
Eve, R. A.; Reddy, B. D.; Rockafellar, R. T.
1990
Nonsmooth analysis and parametric optimization. Zbl 0723.49011
Rockafellar, R. T.
1990
Proto-differentiability of set-valued mappings and its applications in optimization. Zbl 0674.90082
Rockafellar, R. T.
1989
Second-order optimality conditions in nonlinear programming obtained by way of epi-derivatives. Zbl 0698.90070
Rockafellar, R. Tyrrell
1989
Hamiltonian trajectories and duality in the optimal control of linear systems with convex costs. Zbl 0682.49019
Rockafellar, R. T.
1989
Perturbation of generalized Kuhn-Tucker points in finite-dimensional optimization. Zbl 0735.90067
Rockafellar, R. T.
1989
...and 108 more Documents
all top 5

#### Cited by 11,475 Authors

 117 Yao, Jen-Chih 102 Mordukhovich, Boris S. 67 Rockafellar, Ralph Tyrrell 66 Penot, Jean-Paul 64 Zhang, Liwei 63 Yang, Xiaoqi 62 Ceng, Lu-Chuan 61 Borwein, Jonathan Michael 59 Bauschke, Heinz H. 59 Kumam, Poom 57 Boţ, Radu Ioan 56 López-Cerdá, Marco Antonio 53 Thibault, Lionel 50 Noor, Muhammad Aslam 50 Yuan, Xiaoming 47 Wang, Shawn Xianfu 46 Jeyakumar, Vaithilingam 44 Goberna, Miguel Angel 42 Outrata, Jiří V. 41 Martínez-Legaz, Juan-Enrique 41 Wets, Roger Jean-Baptiste 40 Flåm, Sjur Didrik 40 Iusem, Alfredo Noel 39 Papageorgiou, Nikolaos S. 38 Adly, Samir 38 Ioffe, Alexander Davidovich 37 Pham Dinh Tao 37 Seeger, Alberto 36 Théra, Michel A. 36 Nguyen Dong Yen 35 Cho, Yeol Je 34 Hantoute, Abderrahim 34 Sun, Jie 33 Lewis, Adrian S. 31 Attouch, Hedy 31 Chuong, Thai Doan 31 Le Thi, Hoai An 31 Reich, Simeon 31 Sun, Defeng 30 Kruger, Alexander Ya. 29 Dontchev, Asen L. 29 Qi, Liqun 29 Teboulle, Marc 29 Wen, Chingfeng 28 Benson, Harold P. 28 Escudero, Laureano Fernando 28 He, Bingsheng 28 Li, Guoyin 28 Pang, Liping 28 Shapiro, Alexander 28 Volle, Michel 27 Bertsekas, Dimitri Panteli 27 Clarke, Francis H. 27 Daniilidis, Aris 27 Fang, Shu-Cherng 27 Han, Deren 27 Lee, Gue Myung 27 Pang, Jong-Shi 27 Svaiter, Benar Fux 27 Zălinescu, Constantin 26 Burke, James V. 26 Chen, Xiaojun 26 Dinh The Luc 26 Ng, Kung-Fu 26 Toh, Kimchuan 26 Tseng, Paul 25 Cánovas, María Josefa 25 Dempe, Stephan 25 Frankowska, Hélène 25 Kurzhanskiĭ, Aleksandr Borisovich 25 Martínez, José Mario 25 Nam, Nguyen Mau 25 Panagiotopoulos, Panagiotis D. 25 Parra, Juan 25 Qin, Xiaolong 25 Shehu, Yekini 25 Zheng, Xiyin 24 Jefferson, Thomas R. 24 Mahmudov, Elimhan N. 24 Pennanen, Teemu 24 Scott, Carlton H. 24 Takahashi, Wataru 24 Wanka, Gert 24 Ye, Jane J. 23 Ansari, Qamrul Hasan 23 Csetnek, Ernö Robert 23 Durea, Marius 23 Henrion, René 23 Kim, Do Sang 23 Ruszczyński, Andrzej 23 Verma, Ram U. 22 Ben-Tal, Aharon 22 Huang, Nan-Jing 22 Moudafi, Abdellatif 22 Strodiot, Jean-Jacques 22 Vinter, Richard B. 22 Zhou, Jinchuan 21 Beer, Gerald Alan 21 Chen, Jein-Shan 21 Combettes, Patrick L. ...and 11,375 more Authors
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#### Cited in 745 Serials

 970 Journal of Optimization Theory and Applications 579 Mathematical Programming. Series A. Series B 578 Journal of Mathematical Analysis and Applications 434 Optimization 297 European Journal of Operational Research 292 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 284 Journal of Global Optimization 233 SIAM Journal on Optimization 209 Set-Valued and Variational Analysis 205 Computational Optimization and Applications 191 Linear Algebra and its Applications 172 Optimization Letters 159 Annals of Operations Research 148 Journal of Mathematical Economics 143 Nonlinear Analysis. Theory, Methods & Applications 140 Fixed Point Theory and Applications 139 Journal of Economic Theory 136 Mathematical Programming 134 Numerical Functional Analysis and Optimization 127 Transactions of the American Mathematical Society 124 Automatica 120 Applied Mathematics and Computation 105 Journal of Inequalities and Applications 104 Journal of Computational and Applied Mathematics 104 Operations Research Letters 101 Optimization Methods & Software 100 Proceedings of the American Mathematical Society 96 Applied Mathematics and Optimization 96 Abstract and Applied Analysis 90 Journal of Differential Equations 86 Set-Valued Analysis 68 Mathematical Methods of Operations Research 67 Computers & Mathematics with Applications 65 Journal of Approximation Theory 63 Journal of Functional Analysis 62 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 58 Systems & Control Letters 55 Applicable Analysis 55 Computer Methods in Applied Mechanics and Engineering 55 Stochastic Processes and their Applications 51 SIAM Journal on Control and Optimization 51 Computers & Operations Research 51 Positivity 48 Mathematical Notes 48 The Annals of Statistics 48 Numerical Algorithms 48 Journal of Convex Analysis 47 Advances in Mathematics 47 Annali di Matematica Pura ed Applicata. Serie Quarta 47 Journal of Applied Mathematics 46 Archive for Rational Mechanics and Analysis 45 Journal of Scientific Computing 45 The Annals of Applied Probability 44 Fuzzy Sets and Systems 44 Journal of Multivariate Analysis 44 Journal of Mathematical Imaging and Vision 43 Games and Economic Behavior 42 Economic Theory 41 Siberian Mathematical Journal 41 Journal of Industrial and Management Optimization 40 Insurance Mathematics & Economics 40 Mathematical and Computer Modelling 40 Calculus of Variations and Partial Differential Equations 40 Journal of Mathematical Sciences (New York) 40 Journal of Fixed Point Theory and Applications 39 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 38 Kybernetika 38 Cybernetics and Systems Analysis 37 Discrete Applied Mathematics 35 Top 35 Proceedings of the Steklov Institute of Mathematics 34 Numerische Mathematik 34 Mathematical Finance 33 Bulletin of the Australian Mathematical Society 32 Journal of Economic Dynamics & Control 31 International Journal for Numerical Methods in Engineering 31 Journal of Statistical Planning and Inference 31 Cybernetics 31 Automation and Remote Control 31 Mathematical Problems in Engineering 31 Finance and Stochastics 31 Vietnam Journal of Mathematics 30 Applied Mathematics Letters 29 International Journal of Systems Science 29 Mathematics of Operations Research 29 Statistics & Probability Letters 29 SIAM Journal on Imaging Sciences 29 Journal of the Operations Research Society of China 28 Nonlinear Analysis. Hybrid Systems 26 Electronic Journal of Statistics 25 Journal of the Franklin Institute 25 Acta Mathematicae Applicatae Sinica. English Series 24 Communications in Mathematical Physics 24 The Annals of Probability 24 Mathematics and Financial Economics 23 International Journal of Game Theory 23 Mathematical Social Sciences 23 Journal de Mathématiques Pures et Appliquées. Neuvième Série 23 Optimization and Engineering 22 Israel Journal of Mathematics ...and 645 more Serials
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#### Cited in 63 Fields

 5,926 Operations research, mathematical programming (90-XX) 3,942 Calculus of variations and optimal control; optimization (49-XX) 1,844 Numerical analysis (65-XX) 1,661 Operator theory (47-XX) 1,526 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 785 Systems theory; control (93-XX) 629 Probability theory and stochastic processes (60-XX) 627 Functional analysis (46-XX) 616 Convex and discrete geometry (52-XX) 586 Statistics (62-XX) 575 Real functions (26-XX) 500 Partial differential equations (35-XX) 384 Ordinary differential equations (34-XX) 378 Computer science (68-XX) 359 Mechanics of deformable solids (74-XX) 317 Linear and multilinear algebra; matrix theory (15-XX) 286 Global analysis, analysis on manifolds (58-XX) 284 General topology (54-XX) 255 Information and communication theory, circuits (94-XX) 200 Approximations and expansions (41-XX) 196 Measure and integration (28-XX) 156 Dynamical systems and ergodic theory (37-XX) 111 Biology and other natural sciences (92-XX) 95 Combinatorics (05-XX) 93 Mechanics of particles and systems (70-XX) 92 Statistical mechanics, structure of matter (82-XX) 87 Differential geometry (53-XX) 77 Quantum theory (81-XX) 76 Algebraic geometry (14-XX) 58 Fluid mechanics (76-XX) 56 Mathematical logic and foundations (03-XX) 54 Several complex variables and analytic spaces (32-XX) 45 Number theory (11-XX) 37 Harmonic analysis on Euclidean spaces (42-XX) 35 Difference and functional equations (39-XX) 34 Geometry (51-XX) 32 Functions of a complex variable (30-XX) 27 Order, lattices, ordered algebraic structures (06-XX) 25 Integral transforms, operational calculus (44-XX) 24 Integral equations (45-XX) 24 Classical thermodynamics, heat transfer (80-XX) 22 Optics, electromagnetic theory (78-XX) 19 Nonassociative rings and algebras (17-XX) 19 Manifolds and cell complexes (57-XX) 17 History and biography (01-XX) 17 Group theory and generalizations (20-XX) 17 Potential theory (31-XX) 15 Geophysics (86-XX) 13 Field theory and polynomials (12-XX) 13 Topological groups, Lie groups (22-XX) 13 Algebraic topology (55-XX) 11 General and overarching topics; collections (00-XX) 11 Commutative algebra (13-XX) 10 Abstract harmonic analysis (43-XX) 9 Special functions (33-XX) 9 Sequences, series, summability (40-XX) 7 Associative rings and algebras (16-XX) 5 Relativity and gravitational theory (83-XX) 4 Category theory; homological algebra (18-XX) 2 General algebraic systems (08-XX) 2 Mathematics education (97-XX) 1 $$K$$-theory (19-XX) 1 Astronomy and astrophysics (85-XX)

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