Abstract
The problem of maximizing the sum of certain composite functions, where each term is the composition of a convex decreasing function, bounded from below, with a convex function having compact level sets arises in certain single facility location problems with gauge distance functions. We show that this problem is equivalent to a convex maximization problem over a compact convex set and develop a specialized polyhedral annexation procedure to find a global solution for the case when the inside function is a polyhedral norm. As the problem was solved recently only for local solutions, this paper offers an algorithm for finding a global solution. Implementation and testing are not treated in this short communication.
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An earlier version of this paper appeared in the proceedings of a conference on Recent Advances in Global Optimization, C. Floudas and P. Pardalos, eds., Princeton University Press, 1991.
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Tuy, H., Al-Khayyal, F.A. Global optimization of a nonconvex single facility location problem by sequential unconstrained convex minimization. J Glob Optim 2, 61–71 (1992). https://doi.org/10.1007/BF00121302
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DOI: https://doi.org/10.1007/BF00121302