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Journal of Global Optimization

, Volume 58, Issue 3, pp 481–495 | Cite as

Problems with resource allocation constraints and optimization over the efficient set

  • P. T. ThachEmail author
  • T. V. Thang
Article

Abstract

The paper studies a nonlinear optimization problem under resource allocation constraints. Using quasi-gradient duality it is shown that the feasible set of the problem is a singleton (in the case of a single resource) or the set of Pareto efficient solutions of an associated vector maximization problem (in the case of \(k>1\) resources). As a result, a nonlinear optimization problem under resource allocation constraints reduces to an optimization over the efficient set. The latter problem can further be converted into a quasiconvex maximization over a compact convex subset of \(\mathbb{R }^k_+.\) Alternatively, it can be approached as a bilevel program and converted into a monotonic optimization problem in \(\mathbb{R }^k_+.\) In either approach the converted problem falls into a common class of global optimization problems for which several practical solution methods exist when the number \(k\) of resources is relatively small, as it often occurs.

Keywords

Duality Resource allocation constraint Optimization over efficient set Bilevel programming Monotonic optimization 

Mathematics Subject Classification (2000)

90C90 90C30 49N15 

Notes

Acknowledgments

The authors are grateful to Prof. Hoang Tuy for several suggestions and advices which have helped to improve the presentation of a first draft of the paper. Also the authors would like to thank the referees for several useful remarks.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute of MathematicsHanoiVietnam
  2. 2.School of Electric PowerHanoiVietnam

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