Gradients on Sets
Jan Mankau, Friedemann Schuricht

TL;DR
This paper introduces a set-valued gradient concept for locally Lipschitz functions to facilitate nonsmooth optimization, focusing on existence, uniqueness, and approximation of descent directions on sets.
Contribution
It develops a new set-valued gradient framework based on Clarke's generalized gradient for nonsmooth functions, aiding in the design of numerical descent algorithms.
Findings
Establishes existence of descent directions on sets.
Provides conditions for uniqueness of these directions.
Lays groundwork for nonsmooth numerical optimization methods.
Abstract
For a locally Lipschitz continuous function the generalized gradient of Clarke is used to develop some (set-valued) gradient on a set . Existence, uniqueness and some approximation are considered for optimal descent directions on set . The results serve as basis for nonsmooth numerical descent algorithms that can be found in subsequent papers.
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Taxonomy
TopicsOptimization and Variational Analysis · Advanced Numerical Analysis Techniques · Advanced Optimization Algorithms Research
