Multi-parametric disaggregation technique for global optimization of polynomial programming problems

This paper discusses a power-based transformation technique that is especially useful when solving polynomial optimization problems, frequently occurring in science and engineering. The polynomial nonlinear problem is primarily transformed into a suitable reformulated problem containing new sets of...

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Bibliographic Details
Published in:Journal of global optimization Vol. 55; no. 2; pp. 227 - 251
Main Authors: Teles, João P., Castro, Pedro M., Matos, Henrique A.
Format: Journal Article
Language:English
Published: Boston Springer US 01.02.2013
Springer
Springer Nature B.V
Subjects:
Approximation
Computer Science
Costs
Engineering
Heat exchangers
Linear programming
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Maximization
Operations Research/Decision Theory
Optimization
Polynomials
Production planning
Programming
Real Functions
Studies
Transformations
Variables
Polynomial
Signomial
Parameterization
Optimization
Mixed-integer linear programming
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:This paper discusses a power-based transformation technique that is especially useful when solving polynomial optimization problems, frequently occurring in science and engineering. The polynomial nonlinear problem is primarily transformed into a suitable reformulated problem containing new sets of discrete and continuous variables. By applying a term-wise disaggregation scheme combined with multi-parametric elements, an upper/lower bounding mixed-integer linear program can be derived for minimization/maximization problems. It can then be solved to global optimality through standard methods, with the original problem being approximated to a certain precision level, which can be as tight as desired. Furthermore, this technique can also be applied to signomial problems with rational exponents, after a few effortless algebraic transformations. Numerical examples taken from the literature are used to illustrate the effectiveness of the proposed approach.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-011-9809-8