Problems with resource allocation constraints and optimization over the efficient set
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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$k>1$$</EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\mathbb{R }^k_+.$$</EquationSource> </InlineEquation> Alternatively, it can be approached as a bilevel program and converted into a monotonic optimization problem in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\mathbb{R }^k_+.$$</EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$k$$</EquationSource> </InlineEquation> of resources is relatively small, as it often occurs. Copyright Springer Science+Business Media New York 2014
Year of publication: |
2014
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Authors: | Thach, P. ; Thang, T. |
Published in: |
Journal of Global Optimization. - Springer. - Vol. 58.2014, 3, p. 481-495
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Publisher: |
Springer |
Subject: | Duality | Resource allocation constraint | Optimization over efficient set | Bilevel programming | Monotonic optimization |
Saved in:
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