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Journal of Global Optimization

, Volume 37, Issue 1, pp 75–84

First Online: 21 July 2006Received: 31 March 2006Accepted: 21 April 2006

Abstract

The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem SQO. It is NP-hard, and contains the maximum stable set problem in graphs as a special case. In this note, we show that the SQO problem may be reformulated as an exponentially sized linear program LP. This reformulation also suggests a hierarchy of polynomial-time solvable LP’s whose optimal values converge finitely to the optimal value of the SQO problem. The hierarchies of LP relaxations from the literature do not share this finite convergence property for SQO, and we review the relevant counterexamples.

KeywordsLinear programming Standard quadratic optimization Positive polynomials  Download to read the full article text



Autor: E. de Klerk - D. V. Pasechnik

Fuente: https://link.springer.com/







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