On the mixed integer signomial programming problems

This paper proposes an approximate method to solve the mixed integer signomial programming problem, for which the objective function and the constraints may contain product terms with exponents and decision variables, which could be continuous or integral. A linear programming relaxation is derived...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 170; no. 2; pp. 1436 - 1451
Main Author: Chang, Ching-Ter
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 15.11.2005
Elsevier
Subjects:
Calculus of variations and optimal control
Exact sciences and technology
Linearization technique
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming
Numerical methods in mathematical programming, optimization and calculus of variations
Piecewise linear function
Sciences and techniques of general use
Signomial programming
Signomial programming
Linearization technique
Piecewise linear function
Approximate method
Global optimum
Linear programming
Mixed integer programming
Integer programming
Numerical analysis
Applied mathematics
Linearization techniques
Mixed problem
Objective function
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:This paper proposes an approximate method to solve the mixed integer signomial programming problem, for which the objective function and the constraints may contain product terms with exponents and decision variables, which could be continuous or integral. A linear programming relaxation is derived for the problem based on piecewise linearization techniques, which first convert a signomial term into the sum of absolute terms; these absolute terms are then linearized by linearization strategies. In addition, a novel approach is included for solving integer and undefined problems in the logarithmic piecewise technique, which leads to more usefulness of the proposed method. The proposed method could reach a solution as close as possible to the global optimum.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2005.01.034