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

  • Hoang Tuy
  • N. T. Hoai-Phuong
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 84)


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 mn.) 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.

Key words

Global optimization Monotonic optimization, difference of monotonic (d.m.) optimization Composite monotonic constraint Nonconvex optimization Branch-reduce-and-bound method Constrained optimization over the efficient/weakly efficient set Multiplicative constraint Sum-of-ratio constraint 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Hoang Tuy
    • 1
  • N. T. Hoai-Phuong
    • 1
  1. 1.VASTInstitute of MathematicsHanoiVietnam

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