Second-Order Characterizations of Tilt Stability in Composite Optimization

2025/07/15 by Boris S. Mordukhovich, Mordukhovich, Boris S., Peipei Tang +3 · 2 citations
Engineering · #49J52 #49J53 #90C31 #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Topology Optimization in Engineering

paper · pdf · doi:10.48550/arxiv.2507.11253

openalex publication_date 2025/07/15 · openalex created_date 2025/10/08 · openalex updated_date 2026/07/28

Abstract

Tilt stability is a fundamental concept of variational analysis and optimization that plays a pivotal role in both theoretical issues and numerical computations. This paper investigates tilt stability of local minimizers for a general class of composite optimization problems in finite dimensions, where extended-real-valued objectives are compositions of parabolically regular and smooth functions. Under the weakest metric subregularity constraint qualification and other verifiable conditions, we establish unified neighborhood and pointbased characterizations of tilt stability via second-order generalized differentiation. The obtained results provide a rigorous theoretical foundation for further developments on variational stability and numerical algorithms of optimization and related topics.

Citations

• Characterizations of Variational Convexity and Tilt Stability via Quadratic Bundles
• On second-order variational analysis of variational convexity of prox-regular functions
• Perturbation analysis of a class of composite optimization problems
• On (local) analysis of multifunctions via subspaces contained in graphs of generalized derivatives
• Generalized Newton Algorithms for Tilt-Stable Minimizers in Nonsmooth Optimization
• Twice epi-differentiability of extended-real-valued functions with applications in composite optimization
• Parabolic Regularity in Geometric Variational Analysis
• Variational Analysis of Composite Models with Applications to Continuous\n Optimization
• Second-Order Variational Analysis of Parametric Constraint and\n Variational Systems
• Computation of graphical derivatives of normal cone maps to a class of conic constraint sets
• Characterization of tilt stability via subgradient graphical derivative with applications to nonlinear programming
• Complete Characterizations of Tilt Stability in Nonlinear Programming\n under Weakest Qualification Conditions
• Second-order growth, tilt stability, and metric regularity of the subdifferential
• Tilt stability, uniform quadratic growth, and strong metric regularity of the subdifferential
• Second-order subdifferential calculus with applications to tilt stability in optimization

Cited by

• Complete Characterizations of Well-Posedness in Parametric Composite Optimization
• Tilt Stability for Nonlinear Programs under Relaxed Constant Rank Constraint Qualification

Related

• Characterization of tilt stability via subgradient graphical derivative with applications to nonlinear programming
• Complete Characterizations of Tilt Stability in Nonlinear Programming\n under Weakest Qualification Conditions
• Characterizations of Tilt-Stable Minimizers in Second-Order Cone Programming
• Stability Analysis for Composite Optimization Problems and Parametric Variational Systems
• Generalized Newton Algorithms for Tilt-Stable Minimizers in Nonsmooth Optimization