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A rounding procedure for semidefinite optimization

Ali Mohammad-Nezhad(alm413***at***lehigh.edu)
Tamas Terlaky(terlaky***at***lehigh.edu)

Abstract: In this paper, we review the concept of the optimal partition and its identification for semidefinite optimization. In contrast to linear optimization and linear complementarity problem, it is impossible to identify the optimal partition of semidefinite optimization exactly. Instead, the sets of eigenvectors converging to an orthonormal bases for the optimal partition can be identified from an interior solution, which is either a central solution, or a solution in a neighborhood of the central path. Using these sets of eigenvectors, we propose a rounding procedure to generate an approximate maximally complementary solution of semidefinite optimization. The procedure generates a rounded primal-dual solution from an interior solution by solving two least squares problems. We show that if the complementarity gap drops below a certain bound, then the rounded primal-dual solution satisfies the cone constraints.

Keywords: Semidefinite optimization, Optimal partition, Interior point methods, Maximally complementary optimal solution

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: Technical report 17T-009, Industrial and Systems Engineering, Lehigh University, July 2, 2017

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Entry Submitted: 07/03/2017
Entry Accepted: 07/03/2017
Entry Last Modified: 07/03/2017

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