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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Optimization under Composite Monotonic Constraints and Constrained Optimization over the Efficient Set
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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 ℝ
n
with a mapping from ℝ
n
→ ℝ
m
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 ℝ
p
, which can then be efficiently solved by recently developed techniques. Nontrivial numerical examples are presented to illustrate the practicability of the approach.