Edit Profile (opens in new tab) Clarke, Francis H. Compute Distance To: Compute Author ID: clarke.francis-h Published as: Clarke, F. H.; Clarke, Frank H.; Clarke, Francis; Clarke, Francis H.; Clarke, F.; Clarke, Franke H.; Clarke, Frank more...less Homepage: http://math.univ-lyon1.fr/~clarke/ External Links: MGP · Wikidata · GND · IdRef · theses.fr Documents Indexed: 142 Publications since 1972, including 9 Books 3 Contributions as Editor Biographic References: 1 Publication Co-Authors: 30 Co-Authors with 81 Joint Publications 940 Co-Co-Authors all top 5 Co-Authors 63 single-authored 23 Ledyaev, Yuri Semenovich 18 Stern, Ronald Jay 15 Vinter, Richard B. 10 Wolenski, Peter R. 6 Loewen, Philip D. 5 Ekeland, Ivar 4 Aubin, Jean-Pierre 3 de Pinho, Maria do Rosário 3 Radulescu, M. L. 3 Subbotin, Andreĭ Izmaĭlovich 2 Bousquet, Pierre 2 Hiriart-Urruty, Jean-Baptiste 2 Munro, Gordon R. 2 Nour, Chadi 2 Rifford, Ludovic 2 Zeidan, Vera Michel 1 Ancona, Fabio 1 Attouch, Hedy 1 Bessis, D. N. 1 Blagodatskikh, Viktor Ivanovich 1 Bressan, Alberto 1 Cannarsa, Piermarco 1 Clark, Colin W. 1 Demyanov, Vladimir Fedorovich 1 Giannessi, Franco 1 Jamison, Robert E. 1 Moreau, Jean Jacques 1 Raïssi, Nadia 1 Redheffer, Raymond M. 1 Sabidussi, Gert 1 Sontag, Eduardo D. 1 Watkins, Gavin G. all top 5 Serials 18 SIAM Journal on Control and Optimization 9 Transactions of the American Mathematical Society 6 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 5 Journal of Differential Equations 4 Canadian Journal of Mathematics 4 Journal of Convex Analysis 3 Journal of Mathematical Analysis and Applications 3 Applied Mathematics and Optimization 3 Canadian Mathematical Bulletin 3 Control and Cybernetics 3 Proceedings of the American Mathematical Society 3 Systems & Control Letters 3 Nonlinear Analysis. Theory, Methods & Applications 2 Discrete Mathematics 2 IEEE Transactions on Automatic Control 2 Journal of Optimization Theory and Applications 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Discrete and Continuous Dynamical Systems 2 Journal of Dynamical and Control Systems 2 Graduate Texts in Mathematics 1 Archive for Rational Mechanics and Analysis 1 Communications on Pure and Applied Mathematics 1 Advances in Mathematics 1 American Journal of Mathematics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Annales des Sciences Mathématiques du Québec 1 Applied Mathematics Notes 1 Differentsial’nye Uravneniya 1 Econometrica 1 Journal of the London Mathematical Society. Second Series 1 Mathematics of Operations Research 1 Memoirs of the American Mathematical Society 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Pacific Journal of Mathematics 1 Ergodic Theory and Dynamical Systems 1 Applied Mathematics Letters 1 Journal of Global Optimization 1 SIAM Review 1 Bulletin of the Polish Academy of Sciences, Mathematics 1 Mathematical Programming. Series A. Series B 1 Russian Academy of Sciences. Doklady. Mathematics 1 European Journal of Control 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Natural Resource Modeling 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Bulletin of the American Mathematical Society 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 Classics in Applied Mathematics 1 NATO ASI Series. Series C. Mathematical and Physical Sciences 1 Proceedings of the Steklov Institute of Mathematics 1 Series on Advances in Mathematics for Applied Sciences 1 Canadian Mathematical Society Series of Monographs and Advanced Texts 1 Actes des Rencontres du C.I.R.M. all top 5 Fields 118 Calculus of variations and optimal control; optimization (49-XX) 37 Systems theory; control (93-XX) 24 Real functions (26-XX) 21 Ordinary differential equations (34-XX) 12 Operations research, mathematical programming (90-XX) 9 Mechanics of particles and systems (70-XX) 7 Functional analysis (46-XX) 6 Dynamical systems and ergodic theory (37-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 General and overarching topics; collections (00-XX) 4 Partial differential equations (35-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Measure and integration (28-XX) 3 Operator theory (47-XX) 2 Combinatorics (05-XX) 1 Commutative algebra (13-XX) 1 General topology (54-XX) 1 Quantum theory (81-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 123 Publications have been cited 7,627 times in 5,817 Documents Cited by ▼ Year ▼ Optimization and nonsmooth analysis. Zbl 0582.49001Clarke, Frank H. 2,530 1983 Optimization and nonsmooth analysis. Unrev. reprinting of the orig., publ. 1983 by Wiley. Zbl 0727.90045Clarke, F. H. 822 1989 Nonsmooth analysis and control theory. Zbl 1047.49500Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J.; Wolenski, P. R. 644 1998 Optimization and nonsmooth analysis. Reprint. Zbl 0696.49002Clarke, Frank H. 584 1990 Generalized gradients and applications. Zbl 0307.26012Clarke, Frank H. 424 1975 A new approach to Lagrange multipliers. Zbl 0404.90100Clarke, Frank H. 226 1976 Functional analysis, calculus of variations and optimal control. Zbl 1277.49001Clarke, Francis 189 2013 Proximal smoothness and the lower-\(C^ 2\) property. Zbl 0881.49008Clarke, F. H.; Stern, R. J.; Wolenski, P. R. 155 1995 Asymptotic controllability implies feedback stabilization. Zbl 0892.93053Clarke, Francis H.; Ledyaev, Yuri S.; Sontag, Eduardo D.; Subbotin, Andrei I. 132 1997 On the inverse function theorem. Zbl 0331.26013Clarke, F. H. 122 1976 Qualitative properties of trajectories of control systems: a survey. Zbl 0951.49003Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J.; Wolenski, P. R. 117 1995 Hamiltonian trajectories having prescribed minimal period. Zbl 0403.70016Clarke, F. H.; Ekeland, I. 87 1980 Asymptotic stability and smooth Lyapunov functions. Zbl 0907.34013Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 72 1998 Regularity properties of solutions to the basic problem in the calculus of variations. Zbl 0563.49009Clarke, F. H.; Vinter, R. B. 70 1985 Generalized gradients of Lipschitz functionals. Zbl 0463.49017Clarke, Frank H. 68 1981 Periodic solutions to Hamiltonian inclusions. Zbl 0461.34030Clarke, Frank H. 64 1981 The maximum principle under minimal hypotheses. Zbl 0344.49009Clarke, Frank H. 61 1976 Shadow prices and duality for a class of optimal control problems. Zbl 0439.49018Aubin, J. P.; Clarke, F. H. 58 1979 Methods of dynamic and nonsmooth optimization. Zbl 0696.49003Clarke, Frank H. 51 1989 The optimal exploitation of renewable resource stocks: Problems of irreversible investment. Zbl 0396.90026Clark, Colin W.; Clarke, Frank H.; Munro, Gordon R. 45 1979 Nonlinear oscillations and boundary value problems for Hamiltonian systems. Zbl 0514.34032Clarke, Frank H.; Ekeland, I. 42 1982 The relationship between the maximum principle and dynamic programming. Zbl 0642.49014Clarke, Franke H.; Vinter, Richard B 41 1987 Feedback stabilization and Lyapunov functions. Zbl 0961.93047Clarke, F. H.; Ledyaev, Yu. S.; Rifford, L.; Stern, R. J. 37 2000 Optimal multiprocesses. Zbl 0684.49007Clarke, Frank H.; Vinter, Richard B. 31 1989 Subgradient criteria for monotonicity, the Lipschitz condition, and convexity. Zbl 0810.49016Clarke, F. H.; Stern, R. J.; Wolenski, P. R. 31 1993 The Euler-Lagrange differential inclusion. Zbl 0323.49021Clarke, Frank H. 30 1975 Necessary conditions in dynamic optimization. Zbl 1093.49017Clarke, Francis 29 2005 Mean value inequalities in Hilbert space. Zbl 0803.49018Clarke, F. H.; Ledyaev, Yu. S. 28 1994 Approximate invariance and differential inclusions in Hilbert spaces. Zbl 0951.49007Clarke, F. H.; Ledyaev, Yu. S.; Radulescu, M. L. 26 1997 Optimal control problems with mixed constraints. Zbl 1208.49018Clarke, Francis; De Pinho, M. R. 26 2010 A classical variational principle for periodic Hamiltonian trajectories. Zbl 0434.70022Clarke, Frank H. 25 1979 The generalized problem of Bolza. Zbl 0333.49023Clarke, Frank H. 25 1976 Admissible relaxation in variational and control problems. Zbl 0326.49031Clarke, Frank H. 23 1975 An indirect method in the calculus of variations. Zbl 0780.49016Clarke, F. H. 23 1993 Monotone invariant solutions to differential inclusions. Zbl 0405.34049Clarke, Frank H.; Aubin, J.-P. 22 1977 Optimal solutions to differential inclusions. Zbl 0307.49042Clarke, F. H. 21 1976 Applications of optimal multiprocesses. Zbl 0695.49014Clarke, Frank H.; Vinter, Richard B. 21 1989 Regularity, existence and necessary conditions for the basic problem in the calculus of variations. Zbl 0612.49002Clarke, F. H. 21 1987 Local optimality conditions and Lipschitzian solutions to the Hamilton- Jacobi equation. Zbl 0528.49019Clarke, Frank H.; Vinter, Richard B. 20 1983 Continuity of solutions to a basic problem in the calculus of variations. Zbl 1127.49001Clarke, Francis 18 2005 Existence and regularity in the small in the calculus of variations. Zbl 0727.49003Clarke, Frank H.; Vinter, R. B. 18 1985 On the conditions under which the Euler equation or the maximum principle hold. Zbl 0559.49012Clarke, Frank H.; Vinter, R. B. 17 1984 Extremal arcs and extended Hamiltonian systems. Zbl 0369.49011Clarke, Frank H. 17 1977 Optimal control and the true Hamiltonian. Zbl 0408.49025Clarke, Frank H. 17 1979 The value function in optimal control: Sensitivity, controllability, and time-optimality. Zbl 0601.49020Clarke, Frank H.; Loewen, Philip D. 16 1986 Mean value inequalities. Zbl 0856.49017Clarke, F. H.; Ledyaev, Yu. S. 16 1994 Proximal analysis and minimization principles. Zbl 0865.49015Clarke, F. H.; Ledyaev, Yu. S.; Wolenski, P. R. 15 1995 Pointwise contraction criteria for the existence of fixed points. Zbl 0414.54030Clarke, Frank H. 15 1978 A graph polynomial and its applications. Zbl 0244.05111Clarke, Frank H. 15 1972 Necessary conditions, controllability and the value function for differential-difference inclusions. Zbl 0609.49013Clarke, Frank H.; Watkins, Gavin G. 14 1986 Necessary conditions for functional differential inclusions. Zbl 0877.49022Clarke, F. H.; Wolenski, P. R. 13 1996 Gross’ logarithmic Sobolev inequality: A simple proof. Zbl 0421.46029Adams, R. A.; Clarke, Frank H. 12 1979 Local Lipschitz continuity of solutions to a problem in the calculus of variations. Zbl 1141.49033Bousquet, Pierre; Clarke, Francis 12 2007 Optimization and nonsmooth analysis. (Optimizatsiya i negladkij analiz). Transl. from the English by Yu. S. Ledyaev. Transl. ed. by V. I. Blagodatskikh. (Optimizatsiya i negladkij analiz.) Zbl 0662.49001Clarke, Frank H. 12 1988 Partial subdifferentials, derivates and Rademacher’s theorem. Zbl 0924.49013Bessis, D. N.; Clarke, F. H. 12 1999 Feedback in state constrained optimal control. Zbl 1033.49004Clarke, Francis H.; Rifford, Ludovic; Stern, R. J. 12 2002 Sufficiency and the Jacobi condition in the calculus of variations. Zbl 0661.49010Clarke, Frank H.; Zeidan, Vera 12 1986 Solution périodique des équations hamiltoniennes. Zbl 0422.35005Clarke, Frank H. 11 1978 A proximal characterization of the reachable set. Zbl 0866.93008Clarke, F. H. 11 1996 Universal feedback control via proximal aiming in problems of control under disturbance and differential games. Zbl 0965.49022Clarke, F.; Ledyaev, Yu. S.; Subbotin, A. I. 10 1999 Regularity of solutions to variational problems with polynomial Lagrangians. Zbl 0598.49013Clarke, Frank H.; Vinter, Richard B. 10 1986 Regularity properties of optimal controls. Zbl 0715.49039Clarke, F. H.; Vinter, R. B. 10 1990 Fixed points and equilibria in nonconvex sets. Zbl 0840.49010Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 10 1995 Complements, approximations, smoothings and invariance properties. Zbl 0905.49010Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 9 1997 Lyapunov functions and feedback in nonlinear control. Zbl 1079.93037Clarke, Francis 9 2004 Periodic solutions of Hamilton’s equations and local minima of the dual action. Zbl 0596.49030Clarke, Frank H. 9 1985 Multiple integrals of Lipschitz functions in the calculus of variations. Zbl 0411.49015Clarke, Frank H. 9 1977 Differential inclusions with free time. Zbl 0672.49019Loewen, Philip D.; Clarke, Frank H.; Vinter, Richard B. 9 1988 An intermediate existence theory in the calculus of variations. Zbl 0727.49004Clarke, Frank H.; Loewen, Philip D. 9 1989 The Erdmann condition and Hamiltonian inclusions in optimal control and the calculus of variations. Zbl 0461.49007Clarke, Frank H. 8 1980 The synthesis of universal feedback pursuit strategies in differential games. Zbl 0872.90128Clarke, F. H.; Ledyaev, Yu. S.; Subbotin, A. I. 8 1997 Perturbed optimal control problems. Zbl 0587.49026Clarke, Frank H. 8 1986 The maximum principle in optimal control, then and now. Zbl 1167.49311Clarke, Francis 7 2005 State constrained feedback stabilization. Zbl 1037.93068Clarke, F. H.; Stern, R. J. 7 2003 Intersection formulas in nonsmooth analysis. (Formules d’intersection en analyse non lisse.) Zbl 0746.49015Clarke, F. H.; Raissi, N. 7 1990 Control of systems to sets and their interiors. Zbl 0843.93009Clarke, F. H.; Wolenski, P. R. 7 1996 The Hamilton-Jacobi equation of minimal time control. Zbl 1072.49018Clarke, F. H.; Nour, C. 7 2004 Invariance, monotonicity, and applications. Zbl 0936.93001Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 6 1999 Multiplicateurs de Lagrange en optimisation non convexe et applications. Zbl 0365.90105Aubin, Jean-Pierre; Clarke, Frank H. 6 1977 Proximal analysis and feedback construction. Zbl 1116.93031Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 6 2000 Hamiltonian analysis of the generalized problem of Bolza. Zbl 0621.49011Clarke, F. H. 6 1987 The multidirectional mean value theorem in Banach spaces. Zbl 0895.49009Radulescu, M. L.; Clarke, F. H. 5 1997 Multicolorings, measures and games on graphs. Zbl 0328.05110Clarke, F. H.; Jamison, R. E. 5 1976 Inequality constraints in the calculus of variations. Zbl 0337.49012Clarke, Frank H. 5 1977 A Lipschitz regularity theorem. Zbl 1138.49032Clarke, Francis 5 2007 The nonsmooth maximum principle. Zbl 1236.49048Clarke, F.; do Rosario de Pinho, M. 5 2009 On global optimality conditions for nonlinear optimal control problems. Zbl 0944.49020Clarke, F. H.; Hiriart-Urruty, J.-B.; Ledyaev, Yu. S. 5 1998 Hamilton-Jacobi characterization of the state constrained value. Zbl 1098.49005Clarke, F. H.; Stern, R. J. 5 2005 State constraints in optimal control: A case study in proximal normal analysis. Zbl 0637.49007Clarke, Frank H.; Loewen, Philip D. 5 1987 Nonsmooth analysis in control theory: a survey. Zbl 1293.49033Clarke, Francis 5 2001 A decoupling principle in the calculus of variations. Zbl 0795.49018Clarke, F. H. 4 1993 Fixed point theory via nonsmooth analysis. Zbl 0874.47032Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 4 1997 Maximum principles without differentiability. Zbl 0297.49035Clarke, Frank H. 4 1975 Necessary conditions for nonsmooth variational problems. Zbl 0327.49015Clarke, Frank H. 4 1974 The sensitivity of optimal control problems to time delay. Zbl 0769.49022Clarke, F. H.; Wolenski, P. R. 4 1991 Nonconvex duality in optimal control. Zbl 1086.49002Clarke, F. H.; Nour, C. 4 2005 A general theorem on necessary conditions in optimal control. Zbl 1214.49018Clarke, Francis 4 2011 An extension of the Schwarzkopf multiplier rule in optimal control. Zbl 1218.49027Clarke, Francis; Ledyaev, Yuri; de Pinho, Maria do Rosário 4 2011 Nonsmooth analysis and optimization. Zbl 0425.90081Clarke, Frank H. 3 1980 Lagrange multipliers, generalized gradients and calmness. Zbl 0442.49017Clarke, F. H. 3 1980 Functional analysis, calculus of variations and optimal control. Zbl 1277.49001Clarke, Francis 189 2013 A general theorem on necessary conditions in optimal control. Zbl 1214.49018Clarke, Francis 4 2011 An extension of the Schwarzkopf multiplier rule in optimal control. Zbl 1218.49027Clarke, Francis; Ledyaev, Yuri; de Pinho, Maria do Rosário 4 2011 Optimal control problems with mixed constraints. Zbl 1208.49018Clarke, Francis; De Pinho, M. R. 26 2010 The nonsmooth maximum principle. Zbl 1236.49048Clarke, F.; do Rosario de Pinho, M. 5 2009 Stability analysis of sliding-mode feedback control. Zbl 1236.93130Vinter, R.; Clarke, F. 1 2009 Necessary conditions in optimal control and in the calculus of variations. Zbl 1144.49013Clarke, Francis 1 2008 Local Lipschitz continuity of solutions to a problem in the calculus of variations. Zbl 1141.49033Bousquet, Pierre; Clarke, Francis 12 2007 A Lipschitz regularity theorem. Zbl 1138.49032Clarke, Francis 5 2007 Lipschitzian continuity of solutions for a problem in the calculus of variations. (Continuité lipschitzienne des solutions d’un problème en calcul des variations.) Zbl 1134.49023Bousquet, Pierre; Clarke, Francis 1 2006 Necessary conditions in dynamic optimization. Zbl 1093.49017Clarke, Francis 29 2005 Continuity of solutions to a basic problem in the calculus of variations. Zbl 1127.49001Clarke, Francis 18 2005 The maximum principle in optimal control, then and now. Zbl 1167.49311Clarke, Francis 7 2005 Hamilton-Jacobi characterization of the state constrained value. Zbl 1098.49005Clarke, F. H.; Stern, R. J. 5 2005 Nonconvex duality in optimal control. Zbl 1086.49002Clarke, F. H.; Nour, C. 4 2005 Lyapunov and feedback characterizations of state constrained controllability and stabilization. Zbl 1129.93320Clarke, F. H.; Stern, R. J. 3 2005 Lyapunov functions and feedback in nonlinear control. Zbl 1079.93037Clarke, Francis 9 2004 The Hamilton-Jacobi equation of minimal time control. Zbl 1072.49018Clarke, F. H.; Nour, C. 7 2004 State constrained feedback stabilization. Zbl 1037.93068Clarke, F. H.; Stern, R. J. 7 2003 Feedback in state constrained optimal control. Zbl 1033.49004Clarke, Francis H.; Rifford, Ludovic; Stern, R. J. 12 2002 Nonsmooth analysis in control theory: a survey. Zbl 1293.49033Clarke, Francis 5 2001 Feedback stabilization and Lyapunov functions. Zbl 0961.93047Clarke, F. H.; Ledyaev, Yu. S.; Rifford, L.; Stern, R. J. 37 2000 Proximal analysis and feedback construction. Zbl 1116.93031Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 6 2000 The calculus of variations, nonsmooth analysis and optimal control. Zbl 0970.49002Clarke, Francis H. 1 2000 Partial subdifferentials, derivates and Rademacher’s theorem. Zbl 0924.49013Bessis, D. N.; Clarke, F. H. 12 1999 Universal feedback control via proximal aiming in problems of control under disturbance and differential games. Zbl 0965.49022Clarke, F.; Ledyaev, Yu. S.; Subbotin, A. I. 10 1999 Invariance, monotonicity, and applications. Zbl 0936.93001Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 6 1999 Nonsmooth analysis and control theory. Zbl 1047.49500Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J.; Wolenski, P. R. 644 1998 Asymptotic stability and smooth Lyapunov functions. Zbl 0907.34013Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 72 1998 On global optimality conditions for nonlinear optimal control problems. Zbl 0944.49020Clarke, F. H.; Hiriart-Urruty, J.-B.; Ledyaev, Yu. S. 5 1998 Asymptotic controllability implies feedback stabilization. Zbl 0892.93053Clarke, Francis H.; Ledyaev, Yuri S.; Sontag, Eduardo D.; Subbotin, Andrei I. 132 1997 Approximate invariance and differential inclusions in Hilbert spaces. Zbl 0951.49007Clarke, F. H.; Ledyaev, Yu. S.; Radulescu, M. L. 26 1997 Complements, approximations, smoothings and invariance properties. Zbl 0905.49010Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 9 1997 The synthesis of universal feedback pursuit strategies in differential games. Zbl 0872.90128Clarke, F. H.; Ledyaev, Yu. S.; Subbotin, A. I. 8 1997 The multidirectional mean value theorem in Banach spaces. Zbl 0895.49009Radulescu, M. L.; Clarke, F. H. 5 1997 Fixed point theory via nonsmooth analysis. Zbl 0874.47032Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 4 1997 Geometric approximation on proximal normals. Zbl 0908.49016Radulescu, M. L.; Clarke, F. H. 1 1997 Regularity properties of solutions to linear quadratic optimal control problems with state constraints. Zbl 0899.49017Clarke, F. H.; Ledyaev, Y.; Vinter, R. B. 1 1997 Necessary conditions for functional differential inclusions. Zbl 0877.49022Clarke, F. H.; Wolenski, P. R. 13 1996 A proximal characterization of the reachable set. Zbl 0866.93008Clarke, F. H. 11 1996 Control of systems to sets and their interiors. Zbl 0843.93009Clarke, F. H.; Wolenski, P. R. 7 1996 Proximal smoothness and the lower-\(C^ 2\) property. Zbl 0881.49008Clarke, F. H.; Stern, R. J.; Wolenski, P. R. 155 1995 Qualitative properties of trajectories of control systems: a survey. Zbl 0951.49003Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J.; Wolenski, P. R. 117 1995 Proximal analysis and minimization principles. Zbl 0865.49015Clarke, F. H.; Ledyaev, Yu. S.; Wolenski, P. R. 15 1995 Fixed points and equilibria in nonconvex sets. Zbl 0840.49010Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 10 1995 Mean value inequalities in Hilbert space. Zbl 0803.49018Clarke, F. H.; Ledyaev, Yu. S. 28 1994 Mean value inequalities. Zbl 0856.49017Clarke, F. H.; Ledyaev, Yu. S. 16 1994 Subgradient criteria for monotonicity, the Lipschitz condition, and convexity. Zbl 0810.49016Clarke, F. H.; Stern, R. J.; Wolenski, P. R. 31 1993 An indirect method in the calculus of variations. Zbl 0780.49016Clarke, F. H. 23 1993 A decoupling principle in the calculus of variations. Zbl 0795.49018Clarke, F. H. 4 1993 New finite-increment formulas. Zbl 0898.49009Clarke, F. H.; Ledyaev, Yu. S. 3 1993 The proximal subgradient and constancy. Zbl 0804.49014Clarke, F. H.; Redheffer, R. M. 2 1993 The sensitivity of optimal control problems to time delay. Zbl 0769.49022Clarke, F. H.; Wolenski, P. R. 4 1991 Optimization and nonsmooth analysis. Reprint. Zbl 0696.49002Clarke, Frank H. 584 1990 Regularity properties of optimal controls. Zbl 0715.49039Clarke, F. H.; Vinter, R. B. 10 1990 Intersection formulas in nonsmooth analysis. (Formules d’intersection en analyse non lisse.) Zbl 0746.49015Clarke, F. H.; Raissi, N. 7 1990 A regularity theory for variational problems with higher order derivatives. Zbl 0702.49001Clarke, F. H.; Vinter, R. B. 3 1990 Optimization and nonsmooth analysis. Unrev. reprinting of the orig., publ. 1983 by Wiley. Zbl 0727.90045Clarke, F. H. 822 1989 Methods of dynamic and nonsmooth optimization. Zbl 0696.49003Clarke, Frank H. 51 1989 Optimal multiprocesses. Zbl 0684.49007Clarke, Frank H.; Vinter, Richard B. 31 1989 Applications of optimal multiprocesses. Zbl 0695.49014Clarke, Frank H.; Vinter, Richard B. 21 1989 An intermediate existence theory in the calculus of variations. Zbl 0727.49004Clarke, Frank H.; Loewen, Philip D. 9 1989 Variational problems with Lipschitzian minimizers. Zbl 0677.49006Clarke, F. H.; Loewen, P. D. 2 1989 Applications of proximal subgradients. Zbl 0749.49012Clarke, F. H. 1 1989 Optimization and nonsmooth analysis. (Optimizatsiya i negladkij analiz). Transl. from the English by Yu. S. Ledyaev. Transl. ed. by V. I. Blagodatskikh. (Optimizatsiya i negladkij analiz.) Zbl 0662.49001Clarke, Frank H. 12 1988 Differential inclusions with free time. Zbl 0672.49019Loewen, Philip D.; Clarke, Frank H.; Vinter, Richard B. 9 1988 Intermediate existence and regularity in the calculus of variations. Zbl 0695.49001Clarke, Frank H.; Loewen, Philip D. 1 1988 The relationship between the maximum principle and dynamic programming. Zbl 0642.49014Clarke, Franke H.; Vinter, Richard B 41 1987 Regularity, existence and necessary conditions for the basic problem in the calculus of variations. Zbl 0612.49002Clarke, F. H. 21 1987 Hamiltonian analysis of the generalized problem of Bolza. Zbl 0621.49011Clarke, F. H. 6 1987 State constraints in optimal control: A case study in proximal normal analysis. Zbl 0637.49007Clarke, Frank H.; Loewen, Philip D. 5 1987 Coastal states, distant water fishing nations and extended jurisdiction: a principal-agent analysis. Zbl 0850.90174Clarke, F. H.; Munro, G. R. 3 1987 The value function in optimal control: Sensitivity, controllability, and time-optimality. Zbl 0601.49020Clarke, Frank H.; Loewen, Philip D. 16 1986 Necessary conditions, controllability and the value function for differential-difference inclusions. Zbl 0609.49013Clarke, Frank H.; Watkins, Gavin G. 14 1986 Sufficiency and the Jacobi condition in the calculus of variations. Zbl 0661.49010Clarke, Frank H.; Zeidan, Vera 12 1986 Regularity of solutions to variational problems with polynomial Lagrangians. Zbl 0598.49013Clarke, Frank H.; Vinter, Richard B. 10 1986 Perturbed optimal control problems. Zbl 0587.49026Clarke, Frank H. 8 1986 Tonelli’s regularity theory in the calculus of variations: Recent progress. Zbl 0589.49012Clarke, F. H. 2 1986 On connections between the maximum principle and the dynamic programming technique. Zbl 0602.49019Clarke, F. H.; Vinter, R. 2 1986 Regularity properties of solutions to the basic problem in the calculus of variations. Zbl 0563.49009Clarke, F. H.; Vinter, R. B. 70 1985 Existence and regularity in the small in the calculus of variations. Zbl 0727.49003Clarke, Frank H.; Vinter, R. B. 18 1985 Periodic solutions of Hamilton’s equations and local minima of the dual action. Zbl 0596.49030Clarke, Frank H. 9 1985 On the conditions under which the Euler equation or the maximum principle hold. Zbl 0559.49012Clarke, Frank H.; Vinter, R. B. 17 1984 Optimization and nonsmooth analysis. Zbl 0582.49001Clarke, Frank H. 2,530 1983 Local optimality conditions and Lipschitzian solutions to the Hamilton- Jacobi equation. Zbl 0528.49019Clarke, Frank H.; Vinter, Richard B. 20 1983 Nonlinear oscillations and boundary value problems for Hamiltonian systems. Zbl 0514.34032Clarke, Frank H.; Ekeland, I. 42 1982 On Hamiltonian flows and symplectic transformations. Zbl 0506.58012Clarke, Frank H. 2 1982 Generalized gradients of Lipschitz functionals. Zbl 0463.49017Clarke, Frank H. 68 1981 Periodic solutions to Hamiltonian inclusions. Zbl 0461.34030Clarke, Frank H. 64 1981 A variational proof of Aumann’s theorem. Zbl 0518.28007Clarke, Frank H. 1 1981 Hamiltonian trajectories having prescribed minimal period. Zbl 0403.70016Clarke, F. H.; Ekeland, I. 87 1980 The Erdmann condition and Hamiltonian inclusions in optimal control and the calculus of variations. Zbl 0461.49007Clarke, Frank H. 8 1980 Nonsmooth analysis and optimization. Zbl 0425.90081Clarke, Frank H. 3 1980 Lagrange multipliers, generalized gradients and calmness. Zbl 0442.49017Clarke, F. H. 3 1980 Shadow prices and duality for a class of optimal control problems. Zbl 0439.49018Aubin, J. P.; Clarke, F. H. 58 1979 The optimal exploitation of renewable resource stocks: Problems of irreversible investment. Zbl 0396.90026Clark, Colin W.; Clarke, Frank H.; Munro, Gordon R. 45 1979 A classical variational principle for periodic Hamiltonian trajectories. Zbl 0434.70022Clarke, Frank H. 25 1979 Optimal control and the true Hamiltonian. Zbl 0408.49025Clarke, Frank H. 17 1979 Gross’ logarithmic Sobolev inequality: A simple proof. Zbl 0421.46029Adams, R. A.; Clarke, Frank H. 12 1979 Pointwise contraction criteria for the existence of fixed points. Zbl 0414.54030Clarke, Frank H. 15 1978 ...and 23 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,985 Authors 86 Migórski, Stanisław 77 Papageorgiou, Nikolaos S. 54 Thibault, Lionel 51 Qi, Liqun 44 Motreanu, Dumitru 44 Sofonea, Mircea 43 Liu, Zhenhai 42 Clarke, Francis H. 42 Vinter, Richard B. 40 Frankowska, Hélène 39 Mordukhovich, Boris S. 37 Ochal, Anna 35 Penot, Jean-Paul 35 Yao, Jen-Chih 34 Gasiński, Leszek 34 Han, Weimin 34 Nobakhtian, Soghra 34 Panagiotopoulos, Panagiotis D. 32 Yang, Xiaoqi 32 Ye, Jane J. 29 Huang, Lihong 27 Sun, Defeng 26 Noor, Muhammad Aslam 26 Zeng, Shengda 26 Zhang, Liwei 25 Carl, Siegfried 24 Borwein, Jonathan Michael 24 Kanzow, Christian 24 Mahmudov, Elimhan Nadir 24 Mishra, Shashi Kant 24 Outrata, Jiří V. 24 Soleimani-damaneh, Majid 23 Cannarsa, Piermarco 23 Chiou, Suh-Wen 23 Teel, Andrew Richard 22 Bounkhel, Messaoud 22 Xiao, Yibin 21 Chen, Xiaojun 21 Ioffe, Alexander Davidovich 21 Jourani, Abderrahim 21 Lewis, Adrian S. 21 Ma, Changfeng 20 Bagirov, Adil M. 20 Huang, Nan-Jing 20 Wang, Shawn Xianfu 20 Xu, Huifu 20 Zaslavski, Alexander Yakovlevich 18 Arutyunov, Aram Vladimirovic 18 Mariconda, Carlo 18 Zheng, Xiyin 17 Adly, Samir 17 Chen, Jein-Shan 17 Dempe, Stephan 17 Jeyakumar, Vaithilingam 17 Kalita, Piotr 17 Liu, Sanyang 17 Zhou, Jinchuan 16 Aseev, Sergei M. 16 Cai, Zuowei 16 Ekeland, Ivar 16 Ledyaev, Yuri Semenovich 16 Pang, Liping 16 Rockafellar, Ralph Tyrrell 16 Toh, Kim Chuan 16 Nguyen Dong Yen 16 Zeidan, Vera Michel 16 Zeng, Biao 15 Alves, Claudianor Oliveira 15 Bettiol, Piernicola 15 Cao, Jinde 15 Craven, Bruce Desmond 15 Daniilidis, Aris 15 de Pinho, Maria do Rosário 15 Dykhta, Vladimir Aleksandrovich 15 Gao, Yan 15 Li, Chong 15 Naniewicz, Zdzisław 15 Ng, Kung-Fu 15 Nour, Chadi 14 Antczak, Tadeusz 14 Bayón, Luis 14 Burke, James V. 14 Colombo, Giovanni 14 Dinh The Luc 14 Loewen, Philip D. 14 Rădulescu, Vicenţiu D. 14 Rifford, Ludovic 14 Sun, Jie 14 Wu, Soon-Yi 14 Yang, Xinmin 13 Bartosz, Krzysztof 13 Figueiredo, Giovany Malcher 13 Goeleven, Daniel 13 Hiriart-Urruty, Jean-Baptiste 13 Kanzi, Nader 13 Liu, Hongwei 13 Nam, Nguyen Mau 13 Pan, Shaohua 13 Pang, Jong-Shi 13 Stern, Ronald Jay ...and 4,885 more Authors all top 5 Cited in 537 Serials 453 Journal of Optimization Theory and Applications 330 Journal of Mathematical Analysis and Applications 281 Nonlinear Analysis. 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Mathematics 12 Mathematical Control and Related Fields 11 Israel Journal of Mathematics 11 Journal of Approximation Theory 11 SIAM Journal on Numerical Analysis 11 Siberian Mathematical Journal 11 Journal of Information & Optimization Sciences 11 Journal of Elasticity ...and 437 more Serials all top 5 Cited in 55 Fields 2,833 Calculus of variations and optimal control; optimization (49-XX) 2,146 Operations research, mathematical programming (90-XX) 778 Systems theory; control (93-XX) 752 Numerical analysis (65-XX) 661 Partial differential equations (35-XX) 650 Ordinary differential equations (34-XX) 519 Operator theory (47-XX) 347 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 325 Global analysis, analysis on manifolds (58-XX) 323 Real functions (26-XX) 268 Mechanics of deformable solids (74-XX) 243 Functional analysis (46-XX) 180 Dynamical systems and ergodic theory (37-XX) 161 Biology and other natural sciences (92-XX) 112 Computer science (68-XX) 99 General topology (54-XX) 97 Mechanics of particles and systems (70-XX) 96 Convex and discrete geometry (52-XX) 88 Probability theory and stochastic processes (60-XX) 71 Linear and multilinear algebra; matrix theory (15-XX) 71 Differential geometry (53-XX) 70 Statistics (62-XX) 56 Measure and integration (28-XX) 51 Fluid mechanics (76-XX) 41 Approximations and expansions (41-XX) 40 Combinatorics (05-XX) 33 Information and communication theory, circuits (94-XX) 27 Difference and functional equations (39-XX) 17 Algebraic geometry (14-XX) 16 Integral equations (45-XX) 15 Manifolds and cell complexes (57-XX) 12 Optics, electromagnetic theory (78-XX) 11 Quantum theory (81-XX) 11 Statistical mechanics, structure of matter (82-XX) 10 Several complex variables and analytic spaces (32-XX) 9 Mathematical logic and foundations (03-XX) 9 Algebraic topology (55-XX) 8 Classical thermodynamics, heat transfer (80-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Relativity and gravitational theory (83-XX) 5 History and biography (01-XX) 5 Functions of a complex variable (30-XX) 5 Geometry (51-XX) 4 General and overarching topics; collections (00-XX) 4 Nonassociative rings and algebras (17-XX) 4 Integral transforms, operational calculus (44-XX) 4 Geophysics (86-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 2 Topological groups, Lie groups (22-XX) 1 Commutative algebra (13-XX) 1 Category theory; homological algebra (18-XX) 1 Potential theory (31-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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