Semi-algebraic functions have small subdifferentials

DOI10.1007/s10107-012-0624-xzbMath1270.49013arXiv1004.0368OpenAlexW2128908375MaRDI QIDQ359626

Dmitriy Drusvyatskiy, Adrian S. Lewis

Publication date: 12 August 2013

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.0368

zbMATH Keywords

stratificationcritical pointsubdifferentialset-valued mapnondegeneracysemi-algebraic functiontriviality

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53) Set-valued maps in general topology (54C60) Semialgebraic sets and related spaces (14P10) Continuity properties of mappings on manifolds (58C07) Stratifications in topological manifolds (57N80)

Related Items (11)

Partial Smoothness and Constant Rank ⋮ Sweeping by a tame process ⋮ Equations on monotone graphs ⋮ Conservative and semismooth derivatives are equivalent for semialgebraic maps ⋮ Convergence Rate Analysis for Averaged Fixed Point Iterations in Common Fixed Point Problems ⋮ METRIC REGULARITY—A SURVEY PART II. APPLICATIONS ⋮ The dimension of semialgebraic subdifferential graphs ⋮ Convergence rates for boundedly regular systems ⋮ An Application of the Tarski-Seidenberg Theorem with Quantifiers to Vector Variational Inequalities ⋮ Generic Minimizing Behavior in Semialgebraic Optimization ⋮ Clarke Subgradients for Directionally Lipschitzian Stratifiable Functions

Cites Work

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• The dimension of semialgebraic subdifferential graphs
• Monotone (nonlinear) operators in Hilbert space
• Essentially smooth Lipschitz functions
• Geometry of subanalytic and semialgebraic sets
• Geometric categories and o-minimal structures
• Techniques of variational analysis
• Continuity and differentiability of set-valued maps revisited in the light of tame geometry
• Lagrange Multipliers and Optimality
• Generic Optimality Conditions for Semialgebraic Convex Programs
• Clarke Subgradients of Stratifiable Functions
• Critical values of set-valued maps with stratifiable graphs. Extensions of Sard and Smale-Sard theorems
• An Invitation to Tame Optimization
• Optimization and nonsmooth analysis
• On the Construction of Hölder and Proximal Subderivatives
• The Algebraic Geometry of Perfect and Sequential Equilibrium
• Lipschitz functions with prescribed derivatives and subderivatives
• Variational Analysis
• Lipschitz functions with maximal Clarke subdifferentials are generic
• Variational Analysis and Generalized Differentiation I
• The 𝒰-Lagrangian of a convex function
• Prox-regular functions in variational analysis
• Generic nondegeneracy in convex optimization
• Approximating Subdifferentials by Random Sampling of Gradients
• Algorithms in real algebraic geometry

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