Separable standard quadratic optimization problems A standard quadratic optimization problems (StQP) asks for the minimal value of a quadratic form over the standard simplex. StQPs form a central NP-hard class in quadratic optimization and have numerous practical applications. In this note we study the case of a separable objective function and propose an algorithm of worst-case complexity $${\mathcal{O}(n\log n)}$$ . Some extensions to multi-StQPs and ℓ 1−ball constrained problems are also addressed briefly. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Optimization Letters Springer Journals

Optimization Letters, Volume 6 (5) – Mar 26, 2011
10 pages

Publisher
Springer Journals
Subject
Mathematics; Optimization; Operation Research/Decision Theory; Computational Intelligence; Numerical and Computational Physics, Simulation
ISSN
1862-4472
eISSN
1862-4480
D.O.I.
10.1007/s11590-011-0309-z
Publisher site
See Article on Publisher Site

Abstract

A standard quadratic optimization problems (StQP) asks for the minimal value of a quadratic form over the standard simplex. StQPs form a central NP-hard class in quadratic optimization and have numerous practical applications. In this note we study the case of a separable objective function and propose an algorithm of worst-case complexity $${\mathcal{O}(n\log n)}$$ . Some extensions to multi-StQPs and ℓ 1−ball constrained problems are also addressed briefly.

Journal

Published: Mar 26, 2011

References

• The complexity of optimizing over a simplex, hypercube or sphere: a short survey
De Klerk, E.

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