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Handelman rank of zero-diagonal quadratic programs over a hypercube and its applications

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  • Myoung-Ju Park
  • Sung-Pil Hong

Abstract

It has been observed that the Handelman’s certificate of positivity of a polynomial over a compact polyhedron offers a hierarchical relaxation scheme for polynomial programs. The Handelman hierarchy seems particularly suitable for a class of combinatorial optimizations that are formulated as a zero-diagonal quadratic program over a hypercube. In this paper, we present an error analysis of Handelman hierarchy applied to the special class of polynomial programs and its implications in the computation of the combinatorial optimization problems. Copyright Springer Science+Business Media, LLC. 2013

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  • Myoung-Ju Park & Sung-Pil Hong, 2013. "Handelman rank of zero-diagonal quadratic programs over a hypercube and its applications," Journal of Global Optimization, Springer, vol. 56(2), pages 727-736, June.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:2:p:727-736
    DOI: 10.1007/s10898-012-9906-3
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    References listed on IDEAS

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    1. de Klerk, E. & Laurent, M., 2010. "Error bounds for some semidefinite programming approaches to polynomial minimization on the hypercube," Other publications TiSEM 619d9658-77df-4b5e-9868-0, Tilburg University, School of Economics and Management.
    2. William Cook & Sanjeeb Dash, 2001. "On the Matrix-Cut Rank of Polyhedra," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 19-30, February.
    3. Kevin K. H. Cheung, 2007. "Computation of the Lasserre Ranks of Some Polytopes," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 88-94, February.
    4. Jean B. Lasserre, 2002. "Semidefinite Programming vs. LP Relaxations for Polynomial Programming," Mathematics of Operations Research, INFORMS, vol. 27(2), pages 347-360, May.
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