The Subdifferential Descent Method in a Nonsmooth Variational Problem

TL;DR

This paper introduces a subdifferential descent method for solving nonsmooth variational problems with subdifferentiable integrands, providing theoretical proofs and demonstrating the algorithm through examples.

Contribution

It develops and applies a novel subdifferential descent algorithm specifically for nonsmooth variational problems with subdifferentiable integrands.

Findings

Proved subdifferentiability of the functional under natural conditions

Developed a subdifferential descent algorithm for the problem

Demonstrated the algorithm's effectiveness through examples

Abstract

The paper is devoted to the classical variational problem with a nonsmooth integrand of the functional to be minimized. The integrand is supposed to be subdifferentiable. Under some natural conditions the subdifferentiability of the functional considered is proved. The problem of finding the subdifferential descent is being solved and the subdifferential descent method is applied to solve the original problem. The algorithm developed is demonstrated by examples.