A Bilinear Algorithm for Optimizing a Linear Function over the Efficient Set of a Multiple Objective Linear Programming Problem

Jesús Jorge ()

Journal of Global Optimization, 2005, vol. 31, issue 1, 16 pages

Abstract: The problem Q of optimizing a linear function over the efficient set of a multiple objective linear program serves several useful purposes in multiple criteria decision making. However, Q is in itself a difficult global optimization problem, whose local optima, frequently large in number, need not be globally optimal. Indeed, this is due to the fact that the feasible region of Q is, in general, a nonconvex set. In this paper we present a monotonically increasing algorithm that finds an exact, globally-optimal solution for Q. Our approach does not require any hypothesis on the boundedness of neither the efficient set EP nor the optimal objective value. The proposed algorithm relies on a simplified disjoint bilinear program that can be solved through the use of well-known specifically designed methods within nonconvex optimization. The algorithm has been implemented in C and preliminary numerical results are reported. Copyright Springer Science+Business Media New York 2005

Keywords: bilinear programming; global optimization; multiple objective linear programming; optimization over efficient sets (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10898-003-3784-7

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