Univariate parameterization for global optimization of mixed-integer polynomial problems

João P. Teles, Pedro M. Castro and Henrique A. Matos

European Journal of Operational Research, 2013, vol. 229, issue 3, 613-625

Abstract: This paper presents a new relaxation technique to globally optimize mixed-integer polynomial programming problems that arise in many engineering and management contexts. Using a bilinear term as the basic building block, the underlying idea involves the discretization of one of the variables up to a chosen accuracy level (Teles, J.P., Castro, P.M., Matos, H.A. (2013). Multiparametric disaggregation technique for global optimization of polynomial programming problems. J. Glob. Optim. 55, 227–251), by means of a radix-based numeric representation system, coupled with a residual variable to effectively make its domain continuous. Binary variables are added to the formulation to choose the appropriate digit for each position together with new sets of continuous variables and constraints leading to the transformation of the original mixed-integer non-linear problem into a larger one of the mixed-integer linear programming type. The new underestimation approach can be made as tight as desired and is shown capable of providing considerably better lower bounds than a widely used global optimization solver for a specific class of design problems involving bilinear terms.

Keywords: Global optimization; Non-linear programming; Integer programming; Mixed-integer non-linear programming (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221713002750
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:229:y:2013:i:3:p:613-625

DOI: 10.1016/j.ejor.2013.03.042

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().