On a particular quadratic network problem
type: Item
instance of: scholarly article
title: On a particular quadratic network problem
zbMATH Open document ID: 0625.90067
DOI: 10.1016/0377-2217(87)90245-1
author: Ernesto Queirós Vieira Martins
published in: European Journal of Operational Research
publication date: 1987-01-01T00:00:00Z
review text: This paper studies the quadratic function defined by \(f(x)=g(x)+h(x)\) over a convex polyhedron X, where g(x) is a quadratic form. The mathematical background related to quadratic forms and multiobjective programming is presented in Section 2. The problem is studied assuming that g(x) is a positive semidefinite quadratic form. A nonlinear problem arises and three theorems characterize it and an algorithm is given for solving it. A procedure is proposed for implementing the algorithm. The negative semidefiniteness of g(x) fixes another problem which is similarly studied. Two theorems are given and another algorithm is proposed. The study of the indefinite case is accomplished in three theorems that fix the corresponding theory but no algorithm is proposed. The algorithms are multiobjective programming based.
Mathematics Subject Classification ID: 90C20
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 90C35
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 4016605
zbMATH Keywords: convex polyhedron
zbMATH Keywords: quadratic form
zbMATH Keywords: multiobjective programming
reviewed by: S. M. Allende-Alonso
MaRDI profile type: Publication
full work available at URL: 0377-2217(87)90245-1
OpenAlex ID: W1964821805
cites work: A network simplex method
cites work: Q4126046
cites work: Q3734141
cites work: The cyclic method of solving the transshipment problem with an additional linear constraint
cites work: Linear multiobjective programming
description: scientific article; zbMATH DE number 4016605