scientific article
From MaRDI portal
Publication:3952709
zbMath0491.49011MaRDI QIDQ3952709
Publication date: 1980
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
nonsmooth extremal problemsgeneralized normals and derivativesmetric approximationssmoothed unconditional-minimization problems
Numerical mathematical programming methods (65K05) Numerical methods involving duality (49M29) Optimality conditions for minimax problems (49K35) Control/observation systems governed by ordinary differential equations (93C15) Optimality conditions for problems involving ordinary differential equations (49K15) Mathematical programming (90C99)
Related Items
Differential characterizations of covering, metric regularity, and Lipschitzian properties of multifunctions between Banach spaces ⋮ A strong mean value theorem and applications ⋮ Extremal characterizations of asplund spaces ⋮ Maximality and first-order criteria of r-monotone operators ⋮ coderivatives of set-valued mappings: Calculus and applications ⋮ Dualization of the Euler and Hamiltonian inclusions ⋮ Minimax Dirichlet boundary control problem with state constraints ⋮ Approximate subgradients and coderivatives in \(R^ n\) ⋮ Necessary optimality conditions for countably infinite Lipschitz problems with equality constraint mappings ⋮ Characterizations of error bounds for lower semicontinuous functions on metric spaces ⋮ On Higher-Order Sensitivity Analysis of Parametric Henig Set-Valued Equilibrium Problems ⋮ A note on the optimality condition for a bilevel programming ⋮ Variants of the Ekeland variational principle for a set-valued map involving the Clarke normal cone ⋮ Generalized derivatives and nonsmooth optimization, a finite dimensional tour (with comments and rejoinder) ⋮ A Fritz John optimality condition using the approximate subdifferential ⋮ Uniform convexity, uniform monotonicity and \((\phi,c)\)-subdifferentiability with application to nonlinear PDE ⋮ Pseudo metric subregularity and its stability in asplund spaces ⋮ Weak differentiability with applications to variational analysis ⋮ Metric regularity and subdifferential calculus in Banach spaces ⋮ The Ekeland variational principle for Henig proper minimizers and super minimizers ⋮ A note on an approximate Lagrange multiplier rule ⋮ Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market ⋮ Lagrange multipliers theorem and saddle point optimality criteria in mathematical programming ⋮ Solving ill-posed bilevel programs ⋮ Calculus of tangent sets and derivatives of set-valued maps under metric subregularity conditions ⋮ Lipschitzian stability of constraint systems and generalized equations ⋮ Enhanced Karush-Kuhn-Tucker condition and weaker constraint qualifications ⋮ Metric regularity of epigraphical multivalued mappings and applications to vector optimization ⋮ First and second order optimality conditions using approximations for nonsmooth vector optimization in Banach spaces ⋮ Normal subdifferentials of efficient point multifunctions in parametric vector optimization ⋮ Normal and mixed partial second-order subdifferentials in variational analysis and optimization ⋮ Second-order subdifferentials and convexity of real-valued functions ⋮ Clarke coderivatives of efficient point multifunctions in parametric vector optimization ⋮ Qualification conditions for calculus rules of coderivatives of multivalued mappings ⋮ Lipschitzian stability of parametric variational inequalities over generalized polyhedra in Banach spaces ⋮ Fréchet subdifferentials of efficient point multifunctions in parametric vector optimization ⋮ Necessary optimality conditions and exact penalization for non-Lipschitz nonlinear programs ⋮ Hölder metric subregularity for constraint systems in Asplund spaces ⋮ Enhanced Fritz John stationarity, new constraint qualifications and local error bound for mathematical programs with vanishing constraints ⋮ Solution stability of a linearly perturbed constraint system and applications ⋮ Primal-lower-nice property of value functions in optimization and control problems ⋮ Higher-order metric subregularity and its applications ⋮ An Augmented Lagrangian Method for Non-Lipschitz Nonconvex Programming ⋮ Infinite dimensional generalized Jacobian: properties and calculus rules ⋮ Sensitivity analysis of stochastic constraint and variational systems via generalized differentiation ⋮ Subdifferential analysis of differential inclusions via discretization ⋮ On the convergence of coderivative of SAA solution mapping for a parametric stochastic generalized equation ⋮ Discrete approximations and optimization of evolution inclusions ⋮ On the convergence of coderivative of SAA solution mapping for a parametric stochastic variational inequality ⋮ The Ekeland variational principle for set-valued maps involving coderivatives ⋮ A note on implicit multifunction theorems ⋮ Stability and augmented Lagrangian duality in nonconvex semi-infinite programming ⋮ Optimization under generalized equation constraints in Asplund spaces ⋮ Extremal principle based on the linear subdifferential ⋮ Characterization of metric regularity for \({\sigma}\)-subsmooth multifunctions ⋮ Fuzzy calculus for coderivatives of multifunctions ⋮ Mathematical programs with semidefinite cone complementarity constraints: constraint qualifications and optimality conditions ⋮ Stability analysis of stochastic generalized equation via Brouwer's fixed point theorem ⋮ An upper estimate for the Clarke subdifferential of an infimal value function proved via the Mordukhovich subdifferential ⋮ Optimality conditions for various efficient solutions involving coderivatives: from set-valued optimization problems to set-valued equilibrium problems ⋮ Generalized Newton's method based on graphical derivatives ⋮ Controllability and strong controllability of differential inclusions ⋮ Metric regularity, tangential distances and generalized differentiation in Banach spaces ⋮ On Lipschitz semicontinuity properties of variational systems with application to parametric optimization ⋮ Boris Mordukhovich, the never tiring traveller, celebrates his sixtieth birthday ⋮ On metric and calmness qualification conditions in subdifferential calculus ⋮ Openness results for parametric set-valued mappings in Asplund spaces ⋮ Directionally generalized differentiation for multifunctions and applications to set-valued programming problems ⋮ Qualitative properties of trajectories of control systems: a survey ⋮ Gradient consistency for integral-convolution smoothing functions ⋮ New Applications of Variational Analysis to Optimization and Control ⋮ A chain rule for first- and second-order epiderivatives and hypoderivatives ⋮ Complete Characterization of Openness, Metric Regularity, and Lipschitzian Properties of Multifunctions ⋮ Normal coderivative for multifunctions and implicit function theorems ⋮ Generalized Jacobian for functions with infinite dimensional range and domain ⋮ The Lagrange multiplier rule for super efficiency in vector optimization ⋮ Approximating stationary points of stochastic mathematical programs with equilibrium constraints via sample averaging ⋮ Coderivatives of the generalized perturbation maps ⋮ Stability Theory for Parametric Generalized Equations and Variational Inequalities Via Nonsmooth Analysis ⋮ Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints ⋮ Subgradients of the value function to a parametric optimal control problem ⋮ Scalarization and optimality conditions for vector equilibrium problems ⋮ A nonconvex separation property and some applications ⋮ Co-Jacobian for Lipschitzian maps ⋮ On the coderivative of the solution mapping to a second-order cone constrained parametric variational inequality ⋮ Metric regularity of composition set-valued mappings: metric setting and coderivative conditions ⋮ Subdifferential representation formula and subdifferential criteria for the behavior of nonsmooth functions ⋮ Necessary optimality conditions for weak sharp minima in set-valued optimization ⋮ Coderivatives of normal cone mappings and Lipschitzian stability of parametric variational inequalities ⋮ Bornological coderivative and subdifferential calculus in smooth Banach spaces ⋮ Set Optimization—A Rather Short Introduction ⋮ Hölder-Like Property and Metric Regularity of a Positive-Order for Implicit Multifunctions ⋮ Coderivative calculus and metric regularity for constraint and variational systems ⋮ Variational analysis of extended generalized equations via coderivative calculus in Asplund spaces ⋮ Separation theorems for nonconvex sets and application in optimization ⋮ Generalized sequential differential calculus for expected-integral functionals ⋮ First order necessary optimality conditions for mathematical programs with second-order cone complementarity constraints ⋮ Approximate subdifferential and metric regularity: The finite-dimensional case ⋮ First and second-order approximations as derivatives of mappings in optimality conditions for nonsmooth vector optimization ⋮ Second-order characterization of convex functions and its applications ⋮ On the equivalence of some basic principles in variational analysis ⋮ Codifferential calculus ⋮ Nonconvex differential calculus for infinite-dimensional multifunctions ⋮ Computation of graphical derivatives of normal cone maps to a class of conic constraint sets ⋮ Openness properties for parametric set-valued mappings and implicit multifunctions ⋮ Lagrange multipliers for set-valued optimization problems associated with coderivatives ⋮ Optimal control of difference, differential, and differential-difference inclusions ⋮ Variational pairs and applications to stability in nonsmooth analysis. ⋮ Variational analysis and full stability of optimal solutions to constrained and minimax problems ⋮ Lipschitzian inverse functions, directional derivatives, and applications in \(C^{1,1}\) optimization ⋮ Coderivatives of gap function for minty vector variational inequality