Solving semidefinite programming problems via alternating direction methods

Authors:
Zhensheng Yu
Affiliations:
College of Science, University of Shanghai for Science and Technology, Shanghai, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 11
Cited 1

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Semidefinite programming

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Interior-Point Methods for the Monotone Semidefinite Linear Complementarity Problem in Symmetric Matrices

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Primal--Dual Path-Following Algorithms for Semidefinite Programming

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A Superlinearly Convergent Primal-Dual Infeasible-Interior-Point Algorithm for Semidefinite Programming

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Primal-Dual Interior-Point Methods for Semidefinite Programming: Convergence Rates, Stability and Numerical Results

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Alternating direction method for bi-quadratic programming

Journal of Global Optimization

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Abstract

In this paper, we consider an alternating direction algorithm for the solution of semidefinite programming problems (SDP). The main idea of our algorithm is that we reformulate the complementary conditions in the primal--dual optimality conditions as a projection equation. By using this reformulation, we only need to make one projection and solve a linear system of equation with reduced dimension in each iterate. We prove that the generated sequence converges to the solution of the SDP under weak conditions.