On the construction of initial polyhedral convex set for optimization problems over the efficient set and bilevel linear programs
type: Item
instance of: scholarly article
title: On the construction of initial polyhedral convex set for optimization problems over the efficient set and bilevel linear programs
zbMATH Open document ID: 0963.90074
author: Le Dung Muu
published in: Vietnam Journal of Mathematics
publication date: 2001-07-08T00:00:00Z
review text: It is well known that several techniques in optimization require the construction of an initial polyhedral convex set whose vertices and extreme directions are easy to calculate. This short note is devoted to the construction of a well initiated polyhedron meaning that this set contains an optimal solution and is not beyond the domain where the objective function and constraints are defined. For optimization problems over the efficient set of a multiple objective linear program and bilevel linear programs the author makes use of outer and inner approximations for the construction of such a set. In case such a set is neither a simplex, a cone, nor a rectangle, then the author makes use of polyhedral bisection developed in convex-concave programming to obtain a decomposition branch-and-bound algorithm for solving bilevel linear programs.
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 1556841
zbMATH Keywords: well initiated polyhedron
zbMATH Keywords: efficient set
zbMATH Keywords: multiple objective linear program
zbMATH Keywords: bilevel linear programs
zbMATH Keywords: outer and inner approximations
zbMATH Keywords: polyhedral bisection
zbMATH Keywords: decomposition branch-and-bound algorithm
reviewed by: R. N. Kaul
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1556841