On the growth of nonconvex functionals at strict local minimizers

TL;DR

This paper introduces new characterizations of growth conditions at strict local minimizers, including a variant of tilt stability and an analog of the Polyak–Łojasiewicz condition with linear perturbations, advancing understanding of nonconvex functionals.

Contribution

It provides novel characterizations of growth conditions at strict local minimizers, expanding theoretical tools for analyzing nonconvex functionals.

Findings

New characterization of growth conditions at strict local minimizers

Introduction of a variant of tilt stability property

Development of an analog of the Polyak–Łojasiewicz condition with linear perturbations

Abstract

We give new characterizations of growth conditions at strict local minimizers. The main characterizations are a variant of the so-called tilt stability property and an analog of the classical Polyak--\L{}ojasiewicz condition, where the gradient is replaced by linear perturbations.