Optimization under Composite Monotonic Constraints and Constrained Optimization over the Efficient Set

We present a unified approach to a class of nonconvex global optimization problems with composite monotonic constraints. (By composite monotonic function is meant a function which is the composition of a monotonic function on ℝn with a mapping from ℝn → ℝm with m ≤ n.) This class includes problems with constraints involving products of linear functions, sums of ratio functions, etc., and also problems of constrained optimization over efficient/weakly efficient points. The approach is based on transforming the problem into a monotonic optimization problem in the space ℝp, which can then be efficiently solved by recently developed techniques. Nontrivial numerical examples are presented to illustrate the practicability of the approach.

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