An approach to the solution of discontinuous extremal problems
type: Item
instance of: scholarly article
title: An approach to the solution of discontinuous extremal problems
zbMATH Open document ID: 0859.49018
author: V. D. Batukhtin
published in: Journal of Computer and Systems Sciences International
publication date: 1996-06-02T00:00:00Z
review text: An approach to the analysis of discontinuous functions and to the solution of discontinuous extremal problems is described. The approach is based on the so-called approximational gradient. This concept was introduced in the book ``Optimization of discontinuous functions'' (Russian) (1984; Zbl 0535.49001)] published by the author and \textit{L. A. Majboroda}. The approximational gradient is a vector generalizing the concept of subgradient, which is known from the literature. It is used to generalize the basic theorems from differential calculus and optimization (e.g., Fermat, Lagrange, Kuhn-Tucker, and Dubovitskij-Milyutin theorems as well as Pontryagin maximum principle). The author also generalizes the Newton-Kantorovich method for solving operator equations and includes results of some numerical experiments.
reviewed by: Karel Zimmermann
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 880851
zbMATH Keywords: nondifferentiable optimization
zbMATH Keywords: discontinuous extremal problems
zbMATH Keywords: approximational gradient
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 880851