Quadratic growth and critical point stability of semi-algebraic functions

2013/09/05 by Dmitriy Drusvyatskiy, Drusvyatskiy, D., A. D. Ioffe +1 · 2 citations
Mathematics · Medicine · #14P10 #49J52 #49J53 #54C60 #65K10 #90C31 #Advanced Topology and Set Theory #FOS: Mathematics #Functional Equations Stability Results #Lipid metabolism and disorders #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1309.1446

openalex publication_date 2013/09/05 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We show that quadratic growth of a semi-algebraic function is equivalent to strong metric subregularity of the subdifferential --- a kind of stability of generalized critical points. In contrast, this equivalence can easily fail outside of the semi-algebraic setting. As a consequence, we derive necessary conditions and sufficient conditions for optimality in subdifferential terms.

Citations

• Lagrange Multipliers and Optimality
• Numerical optimization

Cited by

• Linear Convergence of a Unified Primal--Dual Algorithm for Convex--Concave Saddle Point Problems with Quadratic Growth
• Generic minimizing behavior in semi-algebraic optimization

Related

• Tilt stability, uniform quadratic growth, and strong metric regularity of the subdifferential
• Quadratic Growth and Strong Metric Subregularity of the Subdifferential for a Class of Non-prox-regular Functions
• Second-order growth, tilt stability, and metric regularity of the subdifferential
• Semi-algebraic functions have small subdifferentials
• Second order optimality conditions for strong local minimizers via subgradient graphical derivative