Calculus Without Derivatives

From MaRDI portal
Publication:2898492

DOI10.1007/978-1-4614-4538-8zbMath1264.49014OpenAlexW591794949MaRDI QIDQ2898492

Jean-Paul Penot

Publication date: 11 July 2012

Published in: Graduate Texts in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4614-4538-8




Related Items

Regularly abstract convex functions with respect to the set of Lipschitz continuous concave functionsStability and Sensitivity Analysis for Quasi-Variational InequalitiesUnnamed ItemUnnamed ItemLyusternik--Graves Theorems for the Sum of a Lipschitz Function and a Set-valued MappingAn Induction Theorem and Nonlinear Regularity ModelsLocal Linear Convergence of the ADMM/Douglas--Rachford Algorithms without Strong Convexity and Application to Statistical ImagingVariational Analysis of Composite Models with Applications to Continuous OptimizationError bounds revisitedDifferential stability of convex discrete optimal control problems with possibly empty solution setsOptimality conditions, approximate stationarity, and applications – a story beyond lipschitznessMaximum entropy and feasibility methods for convex and nonconvex inverse problemsThe Semiconvex Regularization of FunctionsNonlinear metric regularity on fixed setsFréchet differentiability via partial Fréchet differentiabilityInexact proximal point algorithm for quasiconvex optimization problems on Hadamard manifoldsKohn–Sham computation and the bivariate view of density functional theoryFréchet Second-Order Subdifferentials of Lagrangian Functions and Optimality ConditionsENVELOPES FOR SETS AND FUNCTIONS: REGULARIZATION AND GENERALIZED CONJUGACYFuzzy multiplier, sum and intersection rules in non-Lipschitzian settings: decoupling approach revisitedHigher-Order Optimality Conditions and Higher-Order Tangent SetsOn continuous selections of polynomial functionsSecond-order necessary optimality conditions for semilinear elliptic optimal control problemsUnnamed ItemOn some generalized equations with metrically C-increasing mappings: solvability and error bounds with applications to optimizationUnnamed ItemAn induction theorem and Ekeland's variational principle in partial metric spaces with applicationsUnnamed ItemUnnamed ItemUnnamed ItemError Bounds and Multipliers in Constrained Optimization Problems with ToleranceDC approach to weakly convex optimization and nonconvex quadratic optimization problemsUnnamed ItemUnnamed ItemUnnamed ItemSensitivity Analysis of Variational Inequalities via Twice Epi-differentiability and Proto-differentiability of the Proximity OperatorSeparable Reduction of Metric Regularity PropertiesConciliating Generalized DerivativesUnnamed ItemUnnamed ItemMinimal convex majorants of functions and Demyanov–Rubinov exhaustive super(sub)differentialsOn primal regularity estimates for set-valued mappingsCharacterization of quadratic growth of extended-real-valued functionsUnnamed ItemUnnamed ItemUnnamed ItemUnnamed ItemSubdifferential Calculus Rules for Possibly Nonconvex Integral FunctionsA New Constraint Qualification and Sharp Optimality Conditions for Nonsmooth Mathematical Programming Problems in Terms of QuasidifferentialsUnnamed ItemError bounds and metric subregularitySubdifferential Formulae for the Supremum of an Arbitrary Family of FunctionsThe Discrete-Time Geometric Maximum PrincipleUnnamed ItemUnnamed ItemVariational Analysis in Normed Spaces with Applications to Constrained OptimizationInexact Newton Methods and Dennis--Moré Theorems for Nonsmooth Generalized EquationsOn Subgradient ProjectorsFinite-Differential Nonsmooth Speed-Gradient Control: Stability, Passivity, RobustnessPontryagin maximum principle for the optimal control of linearized compressible Navier-Stokes equations with state constraintsGeneralized Farkas' lemma and gap-free duality for minimax DC optimization with polynomials and robust quadratic optimizationPrimal necessary characterizations of transversality propertiesDual sufficient characterizations of transversality propertiesSubgradient methods for sharp weakly convex functionsLinks between functions and subdifferentialsStrongly regular points of mappingsMarket equilibria and moneyVariational analysis of paraconvex multifunctionsOn semiregularity of mappingsHelping you finding an appropriate regularization processOn the relations between some second-order derivativesOn necessary conditions for a minimumSensitivity analysis for expected utility maximization in incomplete Brownian market modelsA strong metric subregularity analysis of nonsmooth mappings via steepest displacement rateCharacterizations of stability of error bounds for convex inequality constraint systemsMoreau-Yosida regularization of state-dependent sweeping processes with nonregular setsContinuous selections for inverse mappings in Banach spacesSome new characterizations of intrinsic transversality in Hilbert spacesDirectional metric pseudo subregularity of set-valued mappings: a general modelStrong metric subregularity of mappings in variational analysis and optimizationSmoothness of the metric projection onto nonconvex bodies in Hilbert spacesLinks between subderivatives and subdifferentialsExistence, iteration procedures and directional differentiability for parabolic QVIsFormulas for asymptotic functions via conjugates, directional derivatives and subdifferentialsSet regularities and feasibility problemsSubdifferentiation of integral functionalsConservative and semismooth derivatives are equivalent for semialgebraic mapsDistance function associated to a prox-regular setOn tangential approximations of the solution set of set-valued inclusionsCharacterizations of the subdifferential of convex integral functions under qualification conditionsSolution stability of a linearly perturbed constraint system and applicationsThe viscosity subdifferential of the rank function via the corresponding subdifferential of its Moreau envelopesOn the variational behaviour of functions with positive steepest descent rateAbout error bounds in metrizable topological vector spacesGeometric and metric characterizations of transversality propertiesDifferential stability of convex optimization problems with possibly empty solution setsOn strong tangential transversalityMetric regularity of quasidifferentiable mappings and optimality conditions for nonsmooth mathematical programming problemsIntegral functionals on nonseparable Banach spaces with applicationsError bounds and Hölder metric subregularityConditions for the stability of ideal efficient solutions in parametric vector optimization via set-valued inclusionsEmergence of price-taking behaviorSeparable reduction in the theory of Fréchet subdifferentialsConvergence of subdifferentials and normal cones in locally uniformly convex Banach spaceOptimal control of a non-smooth semilinear elliptic equationVariational analysis for the consumer theoryThe weak Ekeland variational principle and fixed pointsDirectional differentiability for elliptic quasi-variational inequalities of obstacle typeLocal Lipschitz bounds for solutions to certain singular elliptic equations involving the one-LaplacianA note on the connection between Chaney's derivatives and epi-derivativesFormulae for the conjugate and the subdifferential of the supremum functionQuantitative characterizations of nonconvex bodies with smooth boundaries in Hilbert spaces via the metric projectionRegularity modulus and radius of set-valued mappingsA note on approximate Karush-Kuhn-Tucker conditions in locally Lipschitz multiobjective optimizationNew metric properties for prox-regular setsAbout \([q\)-regularity properties of collections of sets] ⋮ Lipschitz continuity of convex functionsMoreau envelopes of \(s\)-lower regular functionsA variational approach to Lagrange multipliersDirectional Hölder metric regularityNonlinear metric subregularityUpper semismooth functions and the subdifferential determination propertyAbout intrinsic transversality of pairs of setsOn penalty method for equilibrium problems in lexicographic orderImplicit functions: a metric theoryAbout subtransversality of collections of setsRevisiting some rules of convex analysisHigher-order optimality conditions for proper efficiency in nonsmooth vector optimization using radial sets and radial derivativesMetric regularity of the sum of multifunctions and applicationsSecond-order optimality conditions for a semilinear elliptic optimal control problem with mixed pointwise constraintsA convergence analysis of the method of codifferential descentQuantitative characterizations of regularity properties of collections of setsStability results of variational systems under openness with respect to fixed setsNonconvex weak sharp minima on Riemannian manifoldsPreservation of Prox-Regularity of Sets with Applications to Constrained OptimizationA convergent relaxation of the Douglas-Rachford algorithmWell-posedness and subdifferentials of optimal value and infimal convolutionHölder error bounds and Hölder calmness with applications to convex semi-infinite optimizationNEAREST POINTS AND DELTA CONVEX FUNCTIONS IN BANACH SPACESAbstract convex approximations of nonsmooth functionsTransversality properties: primal sufficient conditionsOn the quantitative solution stability of parameterized set-valued inclusionsInterior sphere condition for the graph of a multifunctionMetric inequality conditions on sets and consequences in optimizationNecessary conditions for linear convergence of iterated expansive, set-valued mappingsQuadratic growth and critical point stability of semi-algebraic functionsSecond-order characterization of convex functions and its applicationsExtremality, stationarity and generalized separation of collections of setsDifferential stability properties in convex scalar and vector optimizationSubdifferentials of the marginal functions in parametric convex optimization via intersection formulasOn tangential transversalityThe Lagrangian, constraint qualifications and economicsOn Nash-Moser-Ekeland inverse mapping theoremA versatile approach to metric regularity, openness, and Lipschitzian propertiesSubdifferential stability and subdifferential sum rulesMetric regularity relative to a coneGeneralized resilience and robust statisticsSubdifferentiation of regularized functionsOptimality Conditions in Semidefinite Programming