Maximizing a concave function over the efficient or weakly-efficient set |
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Institution: | 1. Department of Computer Science and Engineering, Indian Institute of Information Technology, Ranchi, Jharkhand, India;2. School of Computer Science and Engineering, Vellore Institute of Technology—AP University, Amaravati, Andhra Pradesh, India;3. Department of Computer Science and Engineering, Indian Institute of Information Technology, Tiruchirappalli, Tamil Nadu, India |
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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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