A Milp Formulation For Generalized Geometric Programming Using Piecewise-Linear Approximations

Keywords

Generalized geometric programming; Gglobal optimization; Mixed-integer linear programming; Piecewise-linear approximation

Abstract

Generalized geometric programming (GGP) problems are converted to mixed-integer linear programming (MILP) problems using piecewise-linear approximations. Our approach is to approximate a multiple-term logsum function of the form log(x1 + x2 +⋯+xn) in terms of a set of linear equalities or inequalities of log x1, log x2, ..., and log xn, where x1, ..., xn are strictly positive. The advantage of this approach is its simplicity and readiness to implement and solve using commercial MILP solvers. While MILP problems in general are no easier than GGP problems, this approach is justified by the phenomenal progress of computing power of both personal computers and commercial MILP solvers. The limitation of this approach is discussed along with numerical tests.

Publication Date

1-1-2015

Publication Title

European Journal of Operational Research

Volume

245

Issue

2

Number of Pages

360-370

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.ejor.2015.01.038

Socpus ID

84933277460 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84933277460

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