One-parameter families of feasible sets in semi-infinite optimization
type: Item
instance of: scholarly article
title: One-parameter families of feasible sets in semi-infinite optimization
zbMATH Open document ID: 0933.90062
DOI: 10.1023/A:1008282216306
published in: Journal of Global Optimization
publication date: 2000-04-02T00:00:00Z
review text: The object of this paper is to show how changes the global topological structure of one-parameter families of feasible sets \(M(t) \subseteq \mathbb{R}^n\) as the parameter \(t \in \mathbb{R} \) varies. The investigations are made for a quite natural class of constraints which describe \(M(t)\) with the following form \[ M^{(H,G,U,V)} (t) = \{ x \in \mathbb{R} ^n \mid h_i(x,t)=0, \;i\in I, \;G(x,y,t) \geq 0, \;y \in Y^{(U,V)}(t) \}, \] where \[ Y^{(U,V)} (t) = \{ y \in \mathbb{R} ^r \mid u_i(y,t)=0, \;i \in A, \;v_j(y,t) \geq 0, \;j \in B \} \] and \(h_i, G, u_i, v_j\) are \(p\)-times continuously differentiable functions. It is shown, that a change in the topological structure is closely related with the violation of some constraint qualification. The authors find out that there are five possible cases for a change in the topological structure of \(M(t)\).
reviewed by: Emil Ivanov
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 90C34
zbMATH DE Number: 1305617
zbMATH Keywords: semi-infinite optimization
zbMATH Keywords: bifurcation point
zbMATH Keywords: feasible set
zbMATH Keywords: constraint qualification
author: Hubertus T. Jongen
author: Jan-Joachim Rückmann
MaRDI profile type: Publication
full work available at URL: a:1008282216306
OpenAlex ID: W199323270
description: scientific article; zbMATH DE number 1305617