Maximizing a concave function over the efficient or weakly-efficient set

Maximizing a concave function over the efficient or weakly-efficient set

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Article ID: iaor20003051
Country: Netherlands
Volume: 117
Issue: 2
Start Page Number: 239
End Page Number: 252
Publication Date: Sep 1999
Journal: European Journal of Operational Research
Authors: ,
Keywords: programming: branch and bound
Abstract:

An important approach in multiple criteria linear programming is the optimization of some function over the efficient or weakly-efficient set. This is a very difficult nonconvex optimization problem, even for the case that the function to be optimized is linear. In this article we consider the problem of maximizing a concave function over the efficient or weakly-efficient set. We show that this problem can essentially be formulated as a special global optimization problem in the space of the extreme criteria of the underlying multiple criteria linear program. An algorithm of branch and bound type is proposed for solving the resulting problem.

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