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

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Global Optimization

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 84))

Summary

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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Author information

Authors and Affiliations

  1. VAST, Institute of Mathematics, 18 Hoang Quoc Viet, 10307, Hanoi, Vietnam

    Hoang Tuy & N. T. Hoai-Phuong

Authors
  1. Hoang Tuy
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  2. N. T. Hoai-Phuong
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Editor information

Editors and Affiliations

  1. Politecnico di Milano, Italia

    Leo Liberti

  2. COPPE, Universidade Federal do Rio de Janiero, Brasil

    Nelson Maculan

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© 2006 Springer Science+Business Media, Inc.

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Tuy, H., Hoai-Phuong, N.T. (2006). Optimization under Composite Monotonic Constraints and Constrained Optimization over the Efficient Set. In: Liberti, L., Maculan, N. (eds) Global Optimization. Nonconvex Optimization and Its Applications, vol 84. Springer, Boston, MA. https://doi.org/10.1007/0-387-30528-9_1

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