Extremal values of a class of functionals with moment constraints
type: Item
instance of: scholarly article
title: Extremal values of a class of functionals with moment constraints
zbMATH Open document ID: 0854.49001
DOI: 10.1007/BF02110381
author: L. N. Polyaev
published in: Mathematical Notes
publication date: 1995-09-25T00:00:00Z
review text: The author investigates the following optimization problem. Let the functions \(u_1 (t), \dots, u_n (t)\), \(w_1 (t), \dots, w_n(t)\) be continuous on \(T = [a,b]\) (or \(T = [a, \infty))\) and linear independent and \(\varphi\) be a continuous function. Let \(\vec u(t)\) and \(\vec w(t)\) denote curves in \(R^{n + 1}\). The problem considered is to find an extremum of the functional \[ J (\sigma) = \varphi \Bigl( \int_T \vec w(t) d \sigma (t) \Bigr) \] in the class of non-decreasing functions, continuous from the right and of bounded variation satisfying the equation \[ c = \int_T \vec u(t) d \sigma (t). \] Sufficient conditions ensuring the existence of the solution are presented and the upper bound for a number of discontinuity points of optimal distribution are found. Three examples are given to illustrate applications of the developed theory.
Mathematics Subject Classification ID: 49J10
Mathematics Subject Classification ID: 49J27
zbMATH DE Number: 797894
zbMATH Keywords: moment constraints
zbMATH Keywords: extremal values
zbMATH Keywords: functionals
zbMATH Keywords: functions of bounded variation
reviewed by: Ernst G. Al'brekht
MaRDI profile type: Publication
cites work: Q5559870
full work available at URL: https://doi.org/10.1007/bf02110381
OpenAlex ID: W2094368742
description: scientific article; zbMATH DE number 797894