Convex programs with several additional reverse convex constraints
type: Item
instance of: scholarly article
title: Convex programs with several additional reverse convex constraints
zbMATH Open document ID: 0609.90091
author: Phan Thien Thach
published in: Acta Mathematica Vietnamica
publication date: 1985-01-01T00:00:00Z
review text: This paper addresses the general problem of minimizing a convex function subject to convex and reverse convex constraints. Here by a reverse convex constraint is meant any constraint of the form g(x)\(\leq 0\), where \(g: R^ n\to R\) is a concave function (i.e. g is a convex function). Clearly, a reverse convex constraint determines a closed subset of \(R^ n\), whose complement is an open convex set (therefore, in the literature such constraints are also termed ''complementary convex''. In the present paper we shall focus our attention on the most typical problem of the mentioned class, namely the following problem \[ (P)\quad Minimize\quad f(x),\quad s.t.\quad x\in D,\quad g(x)\leq 0, \] where \(f: R^ n\to R\) is a convex finite function, D is a closed convex subset of \(R^ n\) given by a convex finite function \(h: R^ n\to R\); \(D=\{x\in R^ n:\) h(x)\(\leq 0\}\), where \(g: R^ n\to R\) is a concave finite function.
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C55
zbMATH DE Number: 3987059
zbMATH Keywords: convex and reverse convex constraints
zbMATH Keywords: complementary convex
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3987059