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Global optimization method for linear multiplicative programming

Global optimization method for linear multiplicative programming In this paper, a new global algorithm is presented to globally solve the linear multiplicative programming (LMP). The problem (LMP) is firstly converted into an equivalent programming problem (LMP (H)) by introducing p auxiliary variables. Then by exploiting structure of (LMP(H)), a linear relaxation programming (LP (H)) of (LMP (H)) is obtained with a problem (LMP) reduced to a sequence of linear programming problems. The algorithm is used to compute the lower bounds called the branch and bound search by solving linear relaxation programming problems (LP(H)). The proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Global optimization method for linear multiplicative programming

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Publisher
Springer Journals
Copyright
Copyright © 2015 by The Editorial Office of AMAS & Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-015-0456-6
Publisher site
See Article on Publisher Site

Abstract

In this paper, a new global algorithm is presented to globally solve the linear multiplicative programming (LMP). The problem (LMP) is firstly converted into an equivalent programming problem (LMP (H)) by introducing p auxiliary variables. Then by exploiting structure of (LMP(H)), a linear relaxation programming (LP (H)) of (LMP (H)) is obtained with a problem (LMP) reduced to a sequence of linear programming problems. The algorithm is used to compute the lower bounds called the branch and bound search by solving linear relaxation programming problems (LP(H)). The proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Jun 19, 2015

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