On a Finite Branch and Bound Algorithm for the Global Minimization of a Concave Power Law Over a Polytope

Vasilios I. Manousiouthakis (), Neil Thomas () and Ahmad M. Justanieah
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Vasilios I. Manousiouthakis: UCLA
Neil Thomas: UCLA
Ahmad M. Justanieah: King Abdul Aziz University

Journal of Optimization Theory and Applications, 2011, vol. 151, issue 1, No 8, 134 pages

Abstract: Abstract In this paper, a finite branch-and-bound algorithm is developed for the minimization of a concave power law over a polytope. Linear terms are also included in the objective function. Using the first order necessary conditions of optimality, the optimization problem is transformed into an equivalent problem consisting of a linear objective function, a set of linear constraints, a set of convex constraints, and a set of bilinear complementary constraints. The transformed problem is then solved using a finite branch-and-bound algorithm that solves two convex problems at each of its nodes. The method is illustrated by means of an example from the literature.

Keywords: N-dimensional polytopes; Nonconvex programming; Global optimization; Branch-and-bound (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10957-011-9863-x

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