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On the Finite Convergence of Successive SDP Relaxation
Methods

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Masakazu Kojima and Levent Tuncel

Let $F$ be a subset of the $n$-dimensional Euclidean space $R^n$
represented in terms of a compact convex subset $C_0$ and a set
$\PC_F$ of finitely or infinitely many quadratic functions on $R^n$
such that $F = \{ \x \in C_0 : p(\x) \leq 0 \ (\forall p(\cdot) \in
\PC_F) \}$. In this paper, we investigate some fundamental properties
related to the finite convergence of the successive SDP (semidefinite
programming) relaxation method proposed by the authors for
approximating the convex hull of $F$.
Research Report B-354, Dept. of Mathematical and Computing
Sciences, Tokyo Institute of Technology, Meguro, Tokyo 152-8552,
Japan, August 1999. Also issued as Research Report CORR 99-36,
Department of Combinatorics and Optimization,
University of Waterloo, Ontario, Canada

Contact: kojma@is.titech.ac.jp