Global Optimization Approach to Optimizing Over the Efficient Set
We consider optimization problem over the efficient set of a linear vector problem where the objective function is a composite convex function of the criteria. We show that in this case the problem can be reduced to a single linear constrained convex maximization or a single convex-concave programming problem. The number of the “nonconvexity variables” in the both reduced forms is just equal to the number of the criteria. Some algoritmic aspects are discussed.
Key WordsOptimization over the Pareto set convex-concave programming convex maximization inner approximation decomposition
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