Edit Profile Clarke, Francis H. Compute Distance To: Compute Author ID: clarke.francis-h Published as: Clarke, F.; Clarke, F. H.; Clarke, Francis; Clarke, Francis H.; Clarke, Frank; Clarke, Frank H.; Clarke, Franke H. Homepage: http://math.univ-lyon1.fr/~clarke/ External Links: MGP · Wikidata Documents Indexed: 145 Publications since 1972, including 12 Books Biographic References: 1 Publication all top 5 Co-Authors 63 single-authored 22 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 Adams, Rick A. 1 Ancona, Fabio 1 Attouch, Hedy 1 Bessis, D. N. 1 Bressan, Alberto 1 Cannarsa, Piermarco 1 Clark, Colin W. 1 Demyanov, Vladimir Fedorovich 1 Giannessi, Franco 1 Jamison, Robert E. 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 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 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 123 Publications have been cited 7,733 times in 5,253 Documents Cited by ▼ Year ▼ Optimization and nonsmooth analysis. Zbl 0582.49001Clarke, Frank H. 2,952 1983 Optimization and nonsmooth analysis. Unrev. reprinting of the orig., publ. 1983 by Wiley. Zbl 0727.90045Clarke, F. H. 811 1989 Nonsmooth analysis and control theory. Zbl 1047.49500Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J.; Wolenski, P. R. 671 1998 Optimization and nonsmooth analysis. Reprint. Zbl 0696.49002Clarke, Frank H. 539 1990 Generalized gradients and applications. Zbl 0307.26012Clarke, Frank H. 377 1975 A new approach to Lagrange multipliers. Zbl 0404.90100Clarke, Frank H. 213 1976 Functional analysis, calculus of variations and optimal control. Zbl 1277.49001Clarke, Francis 138 2013 Proximal smoothness and the lower-\(C^ 2\) property. Zbl 0881.49008Clarke, F. H.; Stern, R. J.; Wolenski, P. R. 128 1995 Asymptotic controllability implies feedback stabilization. Zbl 0892.93053Clarke, Francis H.; Ledyaev, Yuri S.; Sontag, Eduardo D.; Subbotin, Andrei I. 115 1997 Qualitative properties of trajectories of control systems: a survey. Zbl 0951.49003Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J.; Wolenski, P. R. 112 1995 On the inverse function theorem. Zbl 0331.26013Clarke, F. H. 110 1976 Hamiltonian trajectories having prescribed minimal period. Zbl 0403.70016Clarke, F. H.; Ekeland, I. 78 1980 Generalized gradients of Lipschitz functionals. Zbl 0463.49017Clarke, Frank H. 68 1981 Periodic solutions to Hamiltonian inclusions. Zbl 0461.34030Clarke, Frank H. 63 1981 Methods of dynamic and nonsmooth optimization. Zbl 0696.49003Clarke, Frank H. 62 1989 Regularity properties of solutions to the basic problem in the calculus of variations. Zbl 0563.49009Clarke, F. H.; Vinter, R. B. 62 1985 The maximum principle under minimal hypotheses. Zbl 0344.49009Clarke, Frank H. 62 1976 Asymptotic stability and smooth Lyapunov functions. Zbl 0907.34013Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 57 1998 Shadow prices and duality for a class of optimal control problems. Zbl 0439.49018Aubin, J. P.; Clarke, F. H. 55 1979 The optimal exploitation of renewable resource stocks: Problems of irreversible investment. Zbl 0396.90026Clark, Colin W.; Clarke, Frank H.; Munro, Gordon R. 44 1979 Nonlinear oscillations and boundary value problems for Hamiltonian systems. Zbl 0514.34032Clarke, Frank H.; Ekeland, I. 39 1982 The relationship between the maximum principle and dynamic programming. Zbl 0642.49014Clarke, Franke H.; Vinter, Richard B 37 1987 Feedback stabilization and Lyapunov functions. Zbl 0961.93047Clarke, F. H.; Ledyaev, Yu. S.; Rifford, L.; Stern, R. J. 33 2000 Necessary conditions in dynamic optimization. Zbl 1093.49017Clarke, Francis 26 2005 Optimal multiprocesses. Zbl 0684.49007Clarke, Frank H.; Vinter, Richard B. 26 1989 Approximate invariance and differential inclusions in Hilbert spaces. Zbl 0951.49007Clarke, F. H.; Ledyaev, Yu. S.; Radulescu, M. L. 25 1997 Mean value inequalities in Hilbert space. Zbl 0803.49018Clarke, F. H.; Ledyaev, Yu. S. 25 1994 Subgradient criteria for monotonicity, the Lipschitz condition, and convexity. Zbl 0810.49016Clarke, F. H.; Stern, R. J.; Wolenski, P. R. 25 1993 The generalized problem of Bolza. Zbl 0333.49023Clarke, Frank H. 24 1976 The Euler-Lagrange differential inclusion. Zbl 0323.49021Clarke, Frank H. 24 1975 A classical variational principle for periodic Hamiltonian trajectories. Zbl 0434.70022Clarke, Frank H. 23 1979 Admissible relaxation in variational and control problems. Zbl 0326.49031Clarke, Frank H. 23 1975 Regularity, existence and necessary conditions for the basic problem in the calculus of variations. Zbl 0612.49002Clarke, F. H. 21 1987 Monotone invariant solutions to differential inclusions. Zbl 0405.34049Clarke, Frank H.; Aubin, J.-P. 21 1977 Optimal solutions to differential inclusions. Zbl 0307.49042Clarke, F. H. 21 1976 Optimal control problems with mixed constraints. Zbl 1208.49018Clarke, Francis; De Pinho, M. R. 19 2010 Local optimality conditions and Lipschitzian solutions to the Hamilton- Jacobi equation. Zbl 0528.49019Clarke, Frank H.; Vinter, Richard B. 19 1983 An indirect method in the calculus of variations. Zbl 0780.49016Clarke, F. H. 18 1993 Applications of optimal multiprocesses. Zbl 0695.49014Clarke, Frank H.; Vinter, Richard B. 17 1989 On the conditions under which the Euler equation or the maximum principle hold. Zbl 0559.49012Clarke, Frank H.; Vinter, R. B. 17 1984 Optimal control and the true Hamiltonian. Zbl 0408.49025Clarke, Frank H. 17 1979 Extremal arcs and extended Hamiltonian systems. Zbl 0369.49011Clarke, Frank H. 17 1977 The value function in optimal control: Sensitivity, controllability, and time-optimality. Zbl 0601.49020Clarke, Frank H.; Loewen, Philip D. 16 1986 Existence and regularity in the small in the calculus of variations. Zbl 0727.49003Clarke, Frank H.; Vinter, R. B. 16 1985 Continuity of solutions to a basic problem in the calculus of variations. Zbl 1127.49001Clarke, Francis 15 2005 Proximal analysis and minimization principles. Zbl 0865.49015Clarke, F. H.; Ledyaev, Yu. S.; Wolenski, P. R. 15 1995 Mean value inequalities. Zbl 0856.49017Clarke, F. H.; Ledyaev, Yu. S. 14 1994 Necessary conditions, controllability and the value function for differential-difference inclusions. Zbl 0609.49013Clarke, Frank H.; Watkins, Gavin G. 14 1986 Pointwise contraction criteria for the existence of fixed points. Zbl 0414.54030Clarke, Frank H. 14 1978 A graph polynomial and its applications. Zbl 0244.05111Clarke, Frank H. 14 1972 Feedback in state constrained optimal control. Zbl 1033.49004Clarke, Francis H.; Rifford, Ludovic; Stern, R. J. 13 2002 Optimization and nonsmooth analysis. (Optimizatsiya i negladkij analiz). Transl. from the English by Yu. S. Ledyaev. Transl. ed. by V. I. Blagodatskikh. Zbl 0662.49001Clarke, Frank H. 13 1988 Gross’ logarithmic Sobolev inequality: A simple proof. Zbl 0421.46029Adams, R. A.; Clarke, Frank H. 13 1979 A proximal characterization of the reachable set. Zbl 0866.93008Clarke, F. H. 10 1996 Necessary conditions for functional differential inclusions. Zbl 0877.49022Clarke, F. H.; Wolenski, P. R. 10 1996 Fixed points and equilibria in nonconvex sets. Zbl 0840.49010Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 10 1995 Regularity properties of optimal controls. Zbl 0715.49039Clarke, F. H.; Vinter, R. B. 10 1990 An intermediate existence theory in the calculus of variations. Zbl 0727.49004Clarke, Frank H.; Loewen, Philip D. 10 1989 Sufficiency and the Jacobi condition in the calculus of variations. Zbl 0661.49010Clarke, Frank H.; Zeidan, Vera 10 1986 Regularity of solutions to variational problems with polynomial Lagrangians. Zbl 0598.49013Clarke, Frank H.; Vinter, Richard B. 10 1986 Solution périodique des équations hamiltoniennes. Zbl 0422.35005Clarke, Frank H. 10 1978 Local Lipschitz continuity of solutions to a problem in the calculus of variations. Zbl 1141.49033Bousquet, Pierre; Clarke, Francis 9 2007 Partial subdifferentials, derivates and Rademacher’s theorem. Zbl 0924.49013Bessis, D. N.; Clarke, F. H. 9 1999 Periodic solutions of Hamilton’s equations and local minima of the dual action. Zbl 0596.49030Clarke, Frank H. 9 1985 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. 8 1999 Complements, approximations, smoothings and invariance properties. Zbl 0905.49010Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 8 1997 The synthesis of universal feedback pursuit strategies in differential games. Zbl 0872.90128Clarke, F. H.; Ledyaev, Yu. S.; Subbotin, A. I. 8 1997 Differential inclusions with free time. Zbl 0672.49019Loewen, Philip D.; Clarke, Frank H.; Vinter, Richard B. 8 1988 Perturbed optimal control problems. Zbl 0587.49026Clarke, Frank H. 8 1986 Multiple integrals of Lipschitz functions in the calculus of variations. Zbl 0411.49015Clarke, Frank H. 8 1977 The maximum principle in optimal control, then and now. Zbl 1167.49311Clarke, Francis 7 2005 Lyapunov functions and feedback in nonlinear control. Zbl 1079.93037Clarke, Francis 7 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 Control of systems to sets and their interiors. Zbl 0843.93009Clarke, F. H.; Wolenski, P. R. 7 1996 Intersection formulas in nonsmooth analysis. Zbl 0746.49015Clarke, F. H.; Raissi, N. 7 1990 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 Erdmann condition and Hamiltonian inclusions in optimal control and the calculus of variations. Zbl 0461.49007Clarke, Frank H. 6 1980 Multiplicateurs de Lagrange en optimisation non convexe et applications. Zbl 0365.90105Aubin, Jean-Pierre; Clarke, Frank H. 6 1977 Necessary conditions for a general control problem. Zbl 0344.49017Clarke, Frank H. 6 1976 Nonsmooth analysis in control theory: a survey. Zbl 1293.49033Clarke, Francis 5 2001 On global optimality conditions for nonlinear optimal control problems. Zbl 0944.49020Clarke, F. H.; Hiriart-Urruty, J.-B.; Ledyaev, Yu. S. 5 1998 The multidirectional mean value theorem in Banach spaces. Zbl 0895.49009Radulescu, M. L.; Clarke, F. H. 5 1997 State constraints in optimal control: A case study in proximal normal analysis. Zbl 0637.49007Clarke, Frank H.; Loewen, Philip D. 5 1987 Multicolorings, measures and games on graphs. Zbl 0328.05110Clarke, F. H.; Jamison, R. E. 5 1976 Necessary conditions for nonsmooth variational problems. Zbl 0327.49015Clarke, Frank H. 5 1974 A general theorem on necessary conditions in optimal control. Zbl 1214.49018Clarke, Francis 4 2011 A Lipschitz regularity theorem. Zbl 1138.49032Clarke, Francis 4 2007 Nonconvex duality in optimal control. Zbl 1086.49002Clarke, F. H.; Nour, C. 4 2005 Hamilton-Jacobi characterization of the state constrained value. Zbl 1098.49005Clarke, F. H.; Stern, R. J. 4 2005 Invariance, monotonicity, and applications. Zbl 0936.93001Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 4 1999 Fixed point theory via nonsmooth analysis. Zbl 0874.47032Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 4 1997 New finite-increment formulas. Zbl 0898.49009Clarke, F. H.; Ledyaev, Yu. S. 4 1993 The sensitivity of optimal control problems to time delay. Zbl 0769.49022Clarke, F. H.; Wolenski, P. R. 4 1991 Nonsmooth analysis and optimization. Zbl 0425.90081Clarke, Frank H. 4 1980 Inequality constraints in the calculus of variations. Zbl 0337.49012Clarke, Frank H. 4 1977 Maximum principles without differentiability. Zbl 0297.49035Clarke, Frank H. 4 1975 An extension of the Schwarzkopf multiplier rule in optimal control. Zbl 1218.49027Clarke, Francis; Ledyaev, Yuri; de Pinho, Maria do Rosário 3 2011 The nonsmooth maximum principle. Zbl 1236.49048Clarke, F.; do Rosario de Pinho, M. 3 2009 Functional analysis, calculus of variations and optimal control. Zbl 1277.49001Clarke, Francis 138 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 3 2011 Optimal control problems with mixed constraints. Zbl 1208.49018Clarke, Francis; De Pinho, M. R. 19 2010 The nonsmooth maximum principle. Zbl 1236.49048Clarke, F.; do Rosario de Pinho, M. 3 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 9 2007 A Lipschitz regularity theorem. Zbl 1138.49032Clarke, Francis 4 2007 Lipschitzian continuity of solutions for a problem in the calculus of variations. Zbl 1134.49023Bousquet, Pierre; Clarke, Francis 1 2006 Necessary conditions in dynamic optimization. Zbl 1093.49017Clarke, Francis 26 2005 Continuity of solutions to a basic problem in the calculus of variations. Zbl 1127.49001Clarke, Francis 15 2005 The maximum principle in optimal control, then and now. Zbl 1167.49311Clarke, Francis 7 2005 Nonconvex duality in optimal control. Zbl 1086.49002Clarke, F. H.; Nour, C. 4 2005 Hamilton-Jacobi characterization of the state constrained value. Zbl 1098.49005Clarke, F. H.; Stern, R. J. 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 7 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. 13 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. 33 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. 9 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. 8 1999 Invariance, monotonicity, and applications. Zbl 0936.93001Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 4 1999 Nonsmooth analysis and control theory. Zbl 1047.49500Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J.; Wolenski, P. R. 671 1998 Asymptotic stability and smooth Lyapunov functions. Zbl 0907.34013Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 57 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. 115 1997 Approximate invariance and differential inclusions in Hilbert spaces. Zbl 0951.49007Clarke, F. H.; Ledyaev, Yu. S.; Radulescu, M. L. 25 1997 Complements, approximations, smoothings and invariance properties. Zbl 0905.49010Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J. 8 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 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 Geometric approximation on proximal normals. Zbl 0908.49016Radulescu, M. L.; Clarke, F. H. 1 1997 A proximal characterization of the reachable set. Zbl 0866.93008Clarke, F. H. 10 1996 Necessary conditions for functional differential inclusions. Zbl 0877.49022Clarke, F. H.; Wolenski, P. R. 10 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. 128 1995 Qualitative properties of trajectories of control systems: a survey. Zbl 0951.49003Clarke, F. H.; Ledyaev, Yu. S.; Stern, R. J.; Wolenski, P. R. 112 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. 25 1994 Mean value inequalities. Zbl 0856.49017Clarke, F. H.; Ledyaev, Yu. S. 14 1994 Subgradient criteria for monotonicity, the Lipschitz condition, and convexity. Zbl 0810.49016Clarke, F. H.; Stern, R. J.; Wolenski, P. R. 25 1993 An indirect method in the calculus of variations. Zbl 0780.49016Clarke, F. H. 18 1993 New finite-increment formulas. Zbl 0898.49009Clarke, F. H.; Ledyaev, Yu. S. 4 1993 A decoupling principle in the calculus of variations. Zbl 0795.49018Clarke, F. H. 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. 539 1990 Regularity properties of optimal controls. Zbl 0715.49039Clarke, F. H.; Vinter, R. B. 10 1990 Intersection formulas in nonsmooth analysis. 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. 1 1990 Optimization and nonsmooth analysis. Unrev. reprinting of the orig., publ. 1983 by Wiley. Zbl 0727.90045Clarke, F. H. 811 1989 Methods of dynamic and nonsmooth optimization. Zbl 0696.49003Clarke, Frank H. 62 1989 Optimal multiprocesses. Zbl 0684.49007Clarke, Frank H.; Vinter, Richard B. 26 1989 Applications of optimal multiprocesses. Zbl 0695.49014Clarke, Frank H.; Vinter, Richard B. 17 1989 An intermediate existence theory in the calculus of variations. Zbl 0727.49004Clarke, Frank H.; Loewen, Philip D. 10 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. Zbl 0662.49001Clarke, Frank H. 13 1988 Differential inclusions with free time. Zbl 0672.49019Loewen, Philip D.; Clarke, Frank H.; Vinter, Richard B. 8 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 37 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. 2 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 10 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 On connections between the maximum principle and the dynamic programming technique. Zbl 0602.49019Clarke, F. H.; Vinter, R. 2 1986 Tonelli’s regularity theory in the calculus of variations: Recent progress. Zbl 0589.49012Clarke, F. H. 2 1986 Regularity properties of solutions to the basic problem in the calculus of variations. Zbl 0563.49009Clarke, F. H.; Vinter, R. B. 62 1985 Existence and regularity in the small in the calculus of variations. Zbl 0727.49003Clarke, Frank H.; Vinter, R. B. 16 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. 2,952 1983 Local optimality conditions and Lipschitzian solutions to the Hamilton- Jacobi equation. Zbl 0528.49019Clarke, Frank H.; Vinter, Richard B. 19 1983 Nonlinear oscillations and boundary value problems for Hamiltonian systems. Zbl 0514.34032Clarke, Frank H.; Ekeland, I. 39 1982 On Hamiltonian flows and symplectic transformations. Zbl 0506.58012Clarke, Frank H. 1 1982 Generalized gradients of Lipschitz functionals. Zbl 0463.49017Clarke, Frank H. 68 1981 Periodic solutions to Hamiltonian inclusions. Zbl 0461.34030Clarke, Frank H. 63 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. 78 1980 The Erdmann condition and Hamiltonian inclusions in optimal control and the calculus of variations. Zbl 0461.49007Clarke, Frank H. 6 1980 Nonsmooth analysis and optimization. Zbl 0425.90081Clarke, Frank H. 4 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. 55 1979 The optimal exploitation of renewable resource stocks: Problems of irreversible investment. Zbl 0396.90026Clark, Colin W.; Clarke, Frank H.; Munro, Gordon R. 44 1979 A classical variational principle for periodic Hamiltonian trajectories. Zbl 0434.70022Clarke, Frank H. 23 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. 13 1979 Pointwise contraction criteria for the existence of fixed points. Zbl 0414.54030Clarke, Frank H. 14 1978 ...and 23 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,666 Authors 74 Papageorgiou, Nikolaos S. 72 Migórski, Stanisław 49 Qi, Liqun 42 Clarke, Francis H. 41 Vinter, Richard B. 40 Sofonea, Mircea 39 Motreanu, Dumitru 38 Thibault, Lionel 37 Liu, Zhenhai 36 Frankowska, Hélène 34 Mordukhovich, Boris S. 34 Ochal, Anna 34 Penot, Jean-Paul 33 Huang, Lihong 33 Panagiotopoulos, Panagiotis D. 32 Yang, Xiaoqi 31 Gasiński, Leszek 31 Nobakhtian, Soghra 28 Ye, Jane J. 27 Yao, Jen-Chih 26 Carl, Siegfried 26 Sun, Defeng 25 Noor, Muhammad Aslam 24 Borwein, Jonathan Michael 24 Chiou, Suh-Wen 24 Han, Weimin 24 Soleimani-damaneh, Majid 24 Teel, Andrew Richard 24 Zhang, Liwei 23 Kanzow, Christian 23 Outrata, Jiří V. 22 Bounkhel, Messaoud 22 Cannarsa, Piermarco 22 Ioffe, Alexander Davidovich 21 Ma, Changfeng 20 Chen, Xiaojun 20 Lewis, Adrian S. 20 Mishra, Shashi Kant 20 Wang, Shawn Xianfu 20 Xu, Huifu 20 Zaslavski, Alexander Yakovlevich 19 Bagirov, Adil M. 19 Mahmudov, Elimhan N. 18 Cao, Jinde 17 Chen, Jein-Shan 17 Huang, Nan-Jing 17 Jeyakumar, Vaithilingam 17 Kalita, Piotr 17 Liu, Sanyang 17 Rockafellar, Ralph Tyrrell 17 Zheng, Xiyin 16 Ekeland, Ivar 16 Ledyaev, Yuri Semenovich 16 Xiao, Yibin 15 Arutyunov, Aram Vladimirovic 15 Craven, Bruce Desmond 15 Daniilidis, Aris 15 Dykhta, Vladimir Aleksandrovich 15 Naniewicz, Zdzisław 15 Pang, Liping 15 Zeidan, Vera Michel 15 Zhou, Jinchuan 14 Antczak, Tadeusz 14 Aseev, Sergei M. 14 Bayón, Luis 14 Cai, Zuowei 14 Dempe, Stephan 14 Dinh The Luc 14 Gao, Yan 14 Li, Chong 14 Loewen, Philip D. 14 Ng, Kung-Fu 14 Rifford, Ludovic 14 Sun, Jie 14 Toh, Kimchuan 14 Yang, Xinmin 14 Nguyen Dong Yen 13 Adly, Samir 13 Burke, James V. 13 Colombo, Giovanni 13 de Pinho, Maria do Rosário 13 Hiriart-Urruty, Jean-Baptiste 13 Jourani, Abdeljalil 13 Liu, Hongwei 13 Mariconda, Carlo 13 Nam, Nguyen Mau 13 Nour, Chadi 13 Stern, Ronald Jay 13 Suárez, Pedro Maria 12 Azhmyakov, Vadim 12 Barton, Paul I. 12 Bartosz, Krzysztof 12 Figueiredo, Giovany Malcher 12 Goebel, Rafal 12 Kasyanov, Pavlo O. 12 Kim, Do Sang 12 Kristály, Alexandru 12 Kummer, Bernd 12 Mäkelä, Marko Mikael 12 Noll, Dominikus ...and 4,566 more Authors all top 5 Cited in 473 Serials 418 Journal of Optimization Theory and Applications 326 Journal of Mathematical Analysis and Applications 291 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 159 Mathematical Programming. Series A. Series B 142 Nonlinear Analysis. Theory, Methods & Applications 140 Journal of Global Optimization 121 Optimization 100 Systems & Control Letters 97 Numerical Functional Analysis and Optimization 94 Set-Valued and Variational Analysis 92 Automatica 90 Journal of Differential Equations 84 Applied Mathematics and Computation 79 Computational Optimization and Applications 78 Journal of Computational and Applied Mathematics 75 Optimization Letters 72 Applied Mathematics and Optimization 65 Transactions of the American Mathematical Society 64 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 62 SIAM Journal on Optimization 51 Set-Valued Analysis 47 European Journal of Operational Research 47 Nonlinear Analysis. Real World Applications 46 SIAM Journal on Control and Optimization 45 Computers & Mathematics with Applications 42 Abstract and Applied Analysis 42 Optimization Methods & Software 41 Neural Networks 37 Journal of Mathematical Economics 35 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 35 Proceedings of the Steklov Institute of Mathematics 34 Proceedings of the American Mathematical Society 31 Calculus of Variations and Partial Differential Equations 30 Journal of Applied Mathematics and Computing 27 Journal of the Franklin Institute 26 Journal of Mathematical Sciences (New York) 25 International Journal of Control 25 Applied Mathematics Letters 23 Computer Methods in Applied Mechanics and Engineering 23 Journal of Dynamical and Control Systems 22 Positivity 22 Journal of Industrial and Management Optimization 21 Archive for Rational Mechanics and Analysis 21 Journal of Functional Analysis 20 ZAMP. Zeitschrift für angewandte Mathematik und Physik 20 Annali di Matematica Pura ed Applicata. Serie Quarta 20 Journal of Economic Theory 20 International Journal of Robust and Nonlinear Control 19 Mathematical Programming 19 Journal of Convex Analysis 19 European Journal of Control 19 Mathematical Methods of Operations Research 19 Discrete and Continuous Dynamical Systems. Series B 18 Linear Algebra and its Applications 17 Numerical Algorithms 17 Mathematical Problems in Engineering 16 Mathematical Notes 16 Annals of Operations Research 16 Applied Mathematical Modelling 16 International Journal of Computer Mathematics 16 Nonlinear Analysis. Hybrid Systems 15 Applicable Analysis 15 Information Sciences 15 Operations Research Letters 15 Mathematical and Computer Modelling 15 Automation and Remote Control 15 Journal of Inequalities and Applications 15 Journal of Applied Mathematics 14 Mathematische Nachrichten 14 Numerische Mathematik 14 Journal of Economic Dynamics & Control 14 MCSS. Mathematics of Control, Signals, and Systems 14 Russian Mathematics 13 Mathematical Biosciences 13 Acta Mathematicae Applicatae Sinica. English Series 13 Applications of Mathematics 13 Discrete and Continuous Dynamical Systems 13 Vietnam Journal of Mathematics 13 Differential Equations 13 Journal of Systems Science and Complexity 12 Rendiconti del Circolo Matemàtico di Palermo. Serie II 12 Cybernetics 12 Applied Mathematics and Mechanics. (English Edition) 12 Cybernetics and Systems Analysis 12 NoDEA. Nonlinear Differential Equations and Applications 11 Bulletin of the Australian Mathematical Society 11 Journal of Approximation Theory 11 Journal of Information & Optimization Sciences 11 Economic Theory 11 Top 11 Doklady Mathematics 10 Rocky Mountain Journal of Mathematics 10 Chaos, Solitons and Fractals 10 Prikladnaya Matematika i Mekhanika 10 SIAM Journal on Numerical Analysis 10 Siberian Mathematical Journal 10 Computational and Applied Mathematics 10 Acta Mathematica Sinica. English Series 10 Mathematical Control and Related Fields 10 Evolution Equations and Control Theory ...and 373 more Serials all top 5 Cited in 56 Fields 2,587 Calculus of variations and optimal control; optimization (49-XX) 1,929 Operations research, mathematical programming (90-XX) 705 Systems theory; control (93-XX) 655 Numerical analysis (65-XX) 585 Ordinary differential equations (34-XX) 556 Partial differential equations (35-XX) 449 Operator theory (47-XX) 323 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 296 Global analysis, analysis on manifolds (58-XX) 290 Real functions (26-XX) 227 Mechanics of deformable solids (74-XX) 218 Functional analysis (46-XX) 171 Dynamical systems and ergodic theory (37-XX) 153 Biology and other natural sciences (92-XX) 91 General topology (54-XX) 87 Computer science (68-XX) 86 Mechanics of particles and systems (70-XX) 74 Convex and discrete geometry (52-XX) 71 Probability theory and stochastic processes (60-XX) 61 Linear and multilinear algebra; matrix theory (15-XX) 56 Statistics (62-XX) 53 Differential geometry (53-XX) 49 Measure and integration (28-XX) 40 Fluid mechanics (76-XX) 34 Combinatorics (05-XX) 34 Approximations and expansions (41-XX) 27 Difference and functional equations (39-XX) 25 Information and communication theory, circuits (94-XX) 13 Algebraic geometry (14-XX) 11 Integral equations (45-XX) 11 Manifolds and cell complexes (57-XX) 11 Quantum theory (81-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Algebraic topology (55-XX) 9 Optics, electromagnetic theory (78-XX) 8 Mathematical logic and foundations (03-XX) 8 Classical thermodynamics, heat transfer (80-XX) 7 General and overarching topics; collections (00-XX) 7 Several complex variables and analytic spaces (32-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Relativity and gravitational theory (83-XX) 5 History and biography (01-XX) 4 Functions of a complex variable (30-XX) 4 Geophysics (86-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Integral transforms, operational calculus (44-XX) 3 Geometry (51-XX) 2 Nonassociative rings and algebras (17-XX) 2 Topological groups, Lie groups (22-XX) 2 Potential theory (31-XX) 1 General algebraic systems (08-XX) 1 Field theory and polynomials (12-XX) 1 Category theory; homological algebra (18-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. Updates and corrections should be made in Wikidata.