Lyapunov stability of the subgradient method with constant step size
C\'edric Josz, Lexiao Lai
TL;DR
This paper analyzes the stability of the subgradient method with constant step size near local minima for semi-algebraic functions using a novel Lyapunov stability framework.
Contribution
It introduces a new notion of discrete Lyapunov stability and provides necessary and sufficient conditions for stability of the subgradient method.
Findings
Established conditions for stability near local minima.
Provided a theoretical framework for analyzing subgradient method behavior.
Enhanced understanding of convergence properties for semi-algebraic functions.
Abstract
We consider the subgradient method with constant step size for minimizing locally Lipschitz semi-algebraic functions. In order to analyze the behavior of its iterates in the vicinity of a local minimum, we introduce a notion of discrete Lyapunov stability and propose necessary and sufficient conditions for stability.
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Taxonomy
TopicsAdvanced Optimization Algorithms Research · Iterative Methods for Nonlinear Equations · Numerical methods in inverse problems