On global optimization with indefinite quadratics

On global optimization with indefinite quadratics We present an algorithmic framework for global optimization problems in which the non-convexity is manifested as an indefinite-quadratic as part of the objective function. Our solution approach consists of applying a spatial branch-and-bound algorithm, exploiting convexity as much as possible, not only convexity in the constraints, but also extracted from the indefinite-quadratic. A preprocessing stage is proposed to split the indefinite-quadratic into a difference of convex quadratic functions, leading to a more efficient spatial branch-and-bound focused on the isolated non-convexity. We investigate several natural possibilities for splitting an indefinite quadratic at the preprocessing stage, and prove the equivalence of some of them. Through computational experiments with our new solver iquad, we analyze how the splitting strategies affect the performance of our algorithm, and find guidelines for choosing amongst them. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png EURO Journal on Computational Optimization Springer Journals

On global optimization with indefinite quadratics

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2016 by EURO - The Association of European Operational Research Societies
Subject
Business and Management; Operations Research/Decision Theory; Operations Management; Operations Research, Management Science; Optimization
ISSN
2192-4406
eISSN
2192-4414
D.O.I.
10.1007/s13675-016-0079-6
Publisher site
See Article on Publisher Site

Abstract

We present an algorithmic framework for global optimization problems in which the non-convexity is manifested as an indefinite-quadratic as part of the objective function. Our solution approach consists of applying a spatial branch-and-bound algorithm, exploiting convexity as much as possible, not only convexity in the constraints, but also extracted from the indefinite-quadratic. A preprocessing stage is proposed to split the indefinite-quadratic into a difference of convex quadratic functions, leading to a more efficient spatial branch-and-bound focused on the isolated non-convexity. We investigate several natural possibilities for splitting an indefinite quadratic at the preprocessing stage, and prove the equivalence of some of them. Through computational experiments with our new solver iquad, we analyze how the splitting strategies affect the performance of our algorithm, and find guidelines for choosing amongst them.

Journal

EURO Journal on Computational OptimizationSpringer Journals

Published: Dec 21, 2016

References

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