A generalized derivative for calm and stable functions
From MaRDI portal
Publication:1198695
zbMath0787.49007MaRDI QIDQ1198695
Philippe Michel, Jean-Paul Penot
Publication date: 16 January 1993
Published in: Differential and Integral Equations (Search for Journal in Brave)
locally convex topological vector spacemean value theoremchain ruleClarke's generalized gradientradial strict derivativeradial strict subdifferential
Nonsmooth analysis (49J52) Continuity and differentiation questions (26B05) Calculus of vector functions (26B12) Optimality conditions for problems in abstract spaces (49K27)
Related Items
Relating lexicographic smoothness and directed subdifferentiability, Generalized derivatives and nonsmooth optimization, a finite dimensional tour (with comments and rejoinder), Optimality conditions and duality for interval-valued optimization problems using convexifactors, Optimality conditions for pessimistic bilevel problems using convexificator, On constraint qualifications and sensitivity analysis for general optimization problems via pseudo-Jacobians, Necessary optimality conditions in terms of convexificators in Lipschitz optimization, Lagrange multipliers theorem and saddle point optimality criteria in mathematical programming, Contingent derivatives and necessary efficiency conditions for vector equilibrium problems with constraints, New optimality conditions for unconstrained vector equilibrium problem in terms of contingent derivatives in Banach spaces, Convexificators and boundedness of the Kuhn–Tucker multipliers set, Positively homogeneous functions revisited, On semi-infinite mathematical programming problems with equilibrium constraints using generalized convexity, Second-order moderate derivatives, A generalized mean-value theorem and optimality conditions in composite nonsmooth minimization, Constraint qualifications in nonsmooth optimization: Classification and inter-relations, Optimality conditions in optimization problems with convex feasible set using convexificators, On nonsmooth robust multiobjective optimization under generalized convexity with applications to portfolio optimization, Generalized second-order derivatives and optimality conditions, On optimality conditions and duality for multiobjective optimization with equilibrium constraints, Necessary conditions for nonsmooth multiobjective semi-infinite problems using Michel-penot subdifferential, Generalized derivatives and optimality conditions in nonconvex optimization, On Frèchet normal cone for nonsmooth mathematical programming problems with switching constraints, Constraint qualifications in terms of convexificators for nonsmooth programming problems with mixed constraints, First and second-order optimality conditions for nonsmooth vector optimization using set-valued directional derivatives, Optimality conditions for MPECs in terms of directional upper convexifactors, Sufficient optimality conditions and Mond-Weir duality results for a fractional multiobjective optimization problem, On constraint qualifications and optimality conditions for robust optimization problems through pseudo-differential, Scalarization in geometric and functional vector optimization revisited, Optimality conditions in terms of convexificators for a bilevel multiobjective optimization problem, Necessary optimality conditions for bilevel set optimization problems, Sensitivity analysis of the value function for nonsmooth optimization problems, On nonsmooth V-invexity and vector variational-like inequalities in terms of the Michel-Penot subdifferentials, Optimality conditions for a bilevel optimization problem in terms of KKT multipliers and convexificators, Characterization of (weakly/properly/robust) efficient solutions in nonsmooth semi-infinite multiobjective optimization using convexificators, Multiobjective Problems: Enhanced Necessary Conditions and New Constraint Qualifications through Convexificators, Second-order sequence-based necessary optimality conditions in constrained nonsmooth vector optimization and applications, Necessary optimality conditions for a bilevel multiobjective programming problem via a Ψ-reformulation, Ekeland Duality as a Paradigm, Subdifferential test for optimality, Error bounds for systems of lower semicontinuous functions in Asplund spaces, Convexificators and strong Kuhn-Tucker conditions, Softness, sleekness and regularity properties in nonsmooth analysis, Convexifactors, generalized convexity, and optimality conditions, Directional derivatives of Lipschitz functions, Existence and boundedness of the Kuhn-Tucker multipliers in nonsmooth multiobjective optimization, Tangentially ds functions, On necessary optimality conditions for nonsmooth vector optimization problems with mixed constraints in infinite dimensions, Variational subdifferential for quasiconvex functions, Nonsmooth semi-infinite programming problems with mixed constraints, On the Applications of Nonsmooth Vector Optimization Problems to Solve Generalized Vector Variational Inequalities Using Convexificators, Sufficient optimality conditions and duality results for a bilevel multiobjective optimization problem via a Ψ reformulation, Optimality conditions in terms of contingent epiderivatives for strict local Pareto minima in vector optimization problems with constraints, Karush-Kuhn-Tucker Optimality Conditions and Duality for Multiobjective Semi-Infinite Programming Via Tangential Subdifferentials, Optimality conditions for \(\epsilon \)-quasi solutions of optimization problems via \(\epsilon \)-upper convexificators with applications, Optimality conditions for vector optimization problems, Necessary and sufficient optimality conditions for constrained vector equilibrium problems using contingent hypoderivatives, A new Abadie-type constraint qualification for general optimization problems, Optimality conditions for multiobjective fractional programming, via convexificators, Conditioning convex and nonconvex problems, Nonsmooth calculus, minimality, and monotonicity of convexificators, Approximate optimality for quasi approximate solutions in nonsmooth semi-infinite programming problems, using ε-upper semi-regular semi-convexificators, Optimality and duality for nonsmooth minimax programming problems using convexifactor, Approximate generalized Hessians and Taylor’s expansions for continuously Gâteaux differentiable functions, Optimality conditions for nonsmooth semidefinite programming via convexificators
