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SDP vs. LP relaxations for the moment approach in some performance evaluation problems

J.B. Lasserre (lasserre***at***laas.fr)
T. Prieto-Rumeau (tprieto***at***estad.ucm.es)

Abstract: Given a Markov process we are interested in the numerical computation of the moments of the exit time from a bounded domain. We use a moment approach which, together with appropriate semidefinite positivity moment conditions, yields a sequence of semidefinite programs (or SDP relaxations), depending on the number of moments considered, that provide a sequence of nonincreasing (resp. nondecreasing) upper (resp. lower) bounds. The results are compared to the linear Hausdorff moment conditions approach considered in the LP-relaxations of Helmes. The SDP relaxations are shown to be more general and more precise than the LP relaxation

Keywords: LP-relaxations; SDP-relaxations; Semidefinite Programming

Category 1: Applications -- OR and Management Sciences

Category 2: Applications -- OR and Management Sciences (Finance and Economics )

Category 3: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: Stochastic Models 20 (2004), 439--456.

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Entry Submitted: 05/04/2004
Entry Accepted: 05/04/2004
Entry Last Modified: 09/18/2006

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