Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
Lipschitz Behavior of Solutions to Convex Minimization Problems - MaRDI portal

Lipschitz Behavior of Solutions to Convex Minimization Problems

From MaRDI portal
Publication:3328293

DOI10.1287/moor.9.1.87zbMath0539.90085OpenAlexW2097287227WikidataQ95948246 ScholiaQ95948246MaRDI QIDQ3328293

Jean-Pierre Aubin

Publication date: 1984

Published in: Mathematics of Operations Research (Search for Journal in Brave)

Full work available at URL: http://pure.iiasa.ac.at/id/eprint/1685/1/WP-81-076.pdf




Related Items

Differential inclusions with unbounded right-hand side and necessary optimality conditionsLipschitz properties of solutions in mathematical programmingMetric regularity of the feasible set mapping in semi-infinite optimizationMetric regularity and second-order necessary optimality conditions for minimization problems under inclusion constraintsLipschitz behaviour of the Legendre-Fenchel transformA set-valued analysis approach to second order differentiation of nonsmooth functionsQualification conditions for multivalued functions in Banach spaces with applications to nonsmooth vector optimization problemsHölder continuity of solutions to a parametric variational inequalitySemidifferentiable functions and necessary optimality conditionsStable local minimizers in semi-infinite optimization: Regularity and second-order conditionsA note on Lipschitzian stability of variational inequalities over perturbed polyhedral convex setsDirectional differentiability of metric projections onto moving sets at boundary pointsSolving ill-posed bilevel programsNecessary optimality conditions for optimal control problems with nonsmooth mixed state and control constraintsInverse and implicit function theorems for nonsmooth maps in Banach spacesVerifiable necessary and sufficient conditions for openness and regularity of set-valued and single-valued mapsExtended semismooth Newton method for functions with values in a conePerturbation theory of nonlinear programs when the set of optimal solutions is not a singletonA semilocal convergence of a secant-type method for solving generalized equationsConvergence analysis of the Gauss-Newton-type method for Lipschitz-like mappingsProto-differentiability of set-valued mappings and its applications in optimizationSolution sensitivity of a class of variational inequalitiesDirectional Lipschitzian optimal solutions and directional derivative for the optimal value function in nonlinear mathematical programmingStability of the solution set of perturbed nonsmooth inequality systems and applicationScaled constraint qualifications for generalized equation constrained problems and application to nonsmooth mathematical programs with equilibrium constraintsQualification conditions for calculus rules of coderivatives of multivalued mappingsConvex difference criteria for the quantitative stability of parametric quasidifferentiable systemsExtended Newton-type method and its convergence analysis for nonsmooth generalized equationsLipschitz properties of nonsmooth functions and set-valued mappings via generalized differentiationSolution stability of a linearly perturbed constraint system and applicationsA Newton iteration for differentiable set-valued mapsOn the stability and solution sensitivity of a consumer problemAn inverse mapping theorem for \(H\)-differentiable set-valued mapsStability of implicit multifunctions in Banach spacesImplications of the constant rank constraint qualificationCalculus of sequential normal compactness in variational analysis.On constraint qualifications in terms of approximate Jacobians for nonsmooth continuous optimization problemsHölder metric regularity of set-valued mapsRegularity properties of constrained set-valued mappingsOn the convergence of coderivative of SAA solution mapping for a parametric stochastic generalized equationPrederivatives of convex set-valued maps and applications to set optimization problemsSubdifferential of optimal value functions in nonlinear infinite programmingStability and augmented Lagrangian duality in nonconvex semi-infinite programmingThe weak Ekeland variational principle and fixed pointsFirst order optimality conditions for mathematical programs with semidefinite cone complementarity constraintsLocal convergence of some iterative methods for generalized equations.On the Karush-Kuhn-Tucker reformulation of the bilevel optimization problemOptimality conditions for various efficient solutions involving coderivatives: from set-valued optimization problems to set-valued equilibrium problemsOn mappings covering at a nonlinear rate and their perturbation stabilityThe exact penalty principleOn Lipschitz semicontinuity properties of variational systems with application to parametric optimizationSlopes of shadow prices and Lagrange multipliersAn uniparametric secant-type method for nonsmooth generalized equationsDistribution sensitivity in stochastic programmingPseudo-contractivity and metric regularity in fixed point theorySensitivity analysis of a stationary point set map under total perturbations. I: Lipschitzian stabilityOn the solution set of differential inclusions in Banach spaceImplicit mapping theorem for extended metric regularity in metric spacesLipschitz-like property relative to a set and the generalized Mordukhovich criterionLocal convergence of Newton's method for subanalytic variational inclusionsVariational geometry of the complementarity set for second order coneA viscosity solution approach to regularity properties of the optimal value functionConvergence analysis of extended Hummel-Seebeck-type method for solving variational inclusionsSensitivity analysis for nonsmooth generalized equationsOn the Aubin property of a class of parameterized variational systemsBounded Lagrange multiplier rules for general nonsmooth problems and application to mathematical programs with equilibrium constraintsSubgradients of marginal functions in parametric mathematical programmingMetric regularity of the sum of multifunctions and applicationsRelationships between Robinson metric regularity and Lipschitz-like behavior of implicit multifunctionsAn iterative method for semistable solutionsCoderivatives of the generalized perturbation mapsOn the coderivative of the solution mapping to a second-order cone constrained parametric variational inequalityStability and sensitivity-analysis for stochastic programmingMetric regularity, tangent sets, and second-order optimality conditionsVerifiable sufficient conditions for the error bound property of second-order cone complementarity problemsOn the coderivative of the projection operator onto the second-order conePoint-based sufficient conditions for metric regularity of implicit multifunctionsDirectional Lipschitzian optimal solution of infinite-dimensional optimization problemsApproximate subdifferential and metric regularity: The finite-dimensional caseDifferentiable selections and Castaing representations of multifunctionsSubtraction theorems and approximate openness for multifunctions: Topological and infinitesimal viewpointsA new complementarity function and applications in stochastic second-order cone complementarity problemsTikhonov regularization of metrically regular inclusionsSome methods of defining Clarke's coneStable approximations of set-valued mapsAn improved local convergence analysis for a two-step Steffensen-type methodConvergence of the method of chords for solving generalized equationsVariational analysis perspective on linear convergence of some first order methods for nonsmooth convex optimization problemsLipschitz lower semicontinuity moduli for linear inequality systemsOn some regularity properties in variational analysisExtensions of generalized differential calculus in Asplund spacesDirectionally pseudo-Lipschitz set-valued mappingsSome inverse mapping theoremsVariational pairs and applications to stability in nonsmooth analysis.Maximal monotone relations and the second derivatives of nonsmooth functionsHeavy viable trajectories of controlled systemsLimiting behavior of the approximate second-order subdifferential of a convex functionGeneralized convexity and nonsmooth problems of vector optimizationLinear convergence of prox-SVRG method for separable non-smooth convex optimization problems under bounded metric subregularityPerturbation techniques for convergence analysis of proximal gradient method and other first-order algorithms via variational analysisNecessary conditions for extremality and separation theorems with applications to multiobjective optimizationVector variational inequality as a tool for studying vector optimization problemsLipschitz-like mapping and its application to convergence analysis of a variant of Newton's methodMetric Subregularity of Multifunctions: First and Second Order Infinitesimal CharacterizationsContinuity of Optimal Solution Functions and their Conditions on Objective FunctionsRelation between the constant rank and the relaxed constant rank constraint qualificationsPartial Error Bound Conditions and the Linear Convergence Rate of the Alternating Direction Method of MultipliersLipschitzian stability of fully parameterized generalized equationsFirst-Order Optimality Conditions for Mathematical Programs with Second-Order Cone Complementarity ConstraintsExtensions of subgradient calculus with applications to optimizationSensitivity and stability analysis for nonlinear programmingContinuity of the solution map in parametric affine variational inequalitiesLipschitzian stability of constraint systems and generalized equationsMetric regularity and Lipschitzian stability of parametric variational systemsRegularity and strong sufficient optimality conditions in differentiable optimization problemsOn Hölder calmness of minimizing setsMetrically Regular Mapping and Its Utilization to Convergence Analysis of a Restricted Inexact Newton-Type MethodEuler appoximation of the feasible setCoderivatives and Aubin properties of solution mappings for parametric vector variational inequality problemsOn metric regularity of multifunctionsLocal optimality for stationary points of group zero-norm regularized problems and equivalent surrogatesProjectional coderivatives and calculus rulesConvex and nonconvex sweeping processes with velocity constraints: well-posedness and insightsCharacterization of the Robust Isolated Calmness for a Class of Conic Programming ProblemsLipschitz-like property for linear constraint systemsDifferential characterizations of covering, metric regularity, and Lipschitzian properties of multifunctions between Banach spacesUpper-Lipschitz multifunctions and inverse subdifferentialsRelative Lipschitz-like Property of Parametric Systems via Projectional CoderivativesOptimization of the optimal value function in problems of convex parametric programmingContinuous Selections of Solutions to Parametric Variational InequalitiesOn the local surjection propertyEuler-Lagrange and Hamiltonian formalisms in dynamic optimizationMETRIC REGULARITY—A SURVEY PART 1. THEORYFuzzy calculus for coderivatives of multifunctionsMulti-valued graph contraction principle with applicationsOn the Aubin property of solution maps to parameterized variational systems with implicit constraintsDifferential inclusions with measurable-pseudo-Lipschitz right-hand sideOn Lipschitz-like continuity of a class of set-valued mappingsConvergence analysis of a variant of Newton-type method for generalized equationsConvergence analysis of a family of Steffensen-type methods for generalized equationsOn Pseudo-Differentiabilitycoderivatives of set-valued mappings: Calculus and applicationsIsolated zeros of lipschitzian metrically regular -FunctionsComplete Characterization of Openness, Metric Regularity, and Lipschitzian Properties of MultifunctionsNormal coderivative for multifunctions and implicit function theoremsLocal convergence of Newton-like methods for generalized equationsHölder continuity of generalized convex set-valued mappingsHölder continuity of solutions to elastic traffic network modelsNecessary and sufficient conditions for linear suboptimality in constrained optimizationNew Constraint Qualifications for Mathematical Programs with Equilibrium Constraints via Variational AnalysisA general iterative procedure for solving nonsmooth generalized equationsVerifiable Conditions for Openness and Regularity of Multivalued Mappings in Banach SpacesOn a Quantitative Semicontinuity Property of Variational Systems with Applications to Perturbed Quasidifferentiable OptimizationAn Inverse Mapping Theorem for Set-Valued MapsStability Theory for Parametric Generalized Equations and Variational Inequalities Via Nonsmooth AnalysisFirst and second order sensitivity analysis of nonlinear programs under directional constraint qualification conditionsStability analysis of Gauss-type proximal point method for metrically regular mappingsCharacterization of Stochastic Viability of Any Nonsmooth Set Involving Its Generalized Contingent CurvatureQuantitative Analysis for Perturbed Abstract Inequality Systems in Banach SpacesGeneralized differentiation of parameter-dependent sets and mappings†Generalized Second Derivatives of Convex Functions and Saddle FunctionsRegularity of implicit solution mapping to parametric generalized equationCoderivatives and the Solution Map of a Linear Constraint SystemA survey of subdifferential calculus with applicationsUnnamed ItemOn computation of limiting coderivatives of the normal-cone mapping to inequality systems and their applicationsLyusternik-Graves theorem and fixed pointsOn the convergence of extended Newton-type method for solving variational inclusionsPreconditioned proximal point methods and notions of partial subregularityA Hummel–Seebeck type method for variational inclusionsMethods of variational analysis in multiobjective optimizationOn continuous variations of trajectories of differential inclusion with unbounded right-hand sideOn Lipschitzian Properties of Implicit MultifunctionsMetric regularity, openness and Lipschitzian behavior of multifunctionsDirectional Quasi-/Pseudo-Normality as Sufficient Conditions for Metric SubregularityNonconvex differential calculus for infinite-dimensional multifunctionsHölder behavior of optimal solutions and directional differentiability of marginal functions in nonlinear programmingFirst- and Second-Order Epi-Differentiability in Nonlinear ProgrammingSecond-order mollified derivatives and optimizationOptimization and equilibrium problems with equilibrium constraints in infinite-dimensional spacesOptimality Conditions and Stability Analysis via the Mordukhovich SubdifferentialCalmness of constraint systems with applicationsSubgradient of distance functions with applications to Lipschitzian stabilityConstraint Qualifications and Optimality Conditions in Bilevel OptimizationSharp estimates for approximate and exact solutions to quasi-optimization problemsSensitivity analysis for constraint and variational systems by means of set-valued differentiationEpiderivatives of the marginal function in nonsmooth parametric optimizationConvergence analysis of a method for variational inclusionsA TRANSFORMATION METHOD FOR SOLVING THE HAMILTON–JACOBI–BELLMAN EQUATION FOR A CONSTRAINED DYNAMIC STOCHASTIC OPTIMAL ALLOCATION PROBLEMOpenness, Hölder Metric Regularity, and Hölder Continuity Properties of Semialgebraic Set-Valued MapsLipschitzian properties of multifunctionsDifferentiability of the argmin function and a minimum principle for semiconcave subsolutions