A Polynomial Time Constraint-Reduced Algorithm for Semidefinite Optimization Problems
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We present an infeasible primal-dual interior point method for semidefinite optimization problems, making use of constraint reduction. We show that the algorithm is globally convergent and has polynomial complexity, the first such complexity result for primal-dual constraint reduction algorithms for any class of problems. Our algorithm is a modification of one with no constraint reduction due to Potra and Sheng (1998) and can be applied whenever the data matrices are block diagonal. It thus solves as special cases any optimization problem that is a linear, convex quadratic, convex quadratically constrained, or second-order cone problem.
KeywordsSemidefinite programming Interior point methods Constraint reduction Primal dual infeasible Polynomial complexity
Mathematics Subject Classification90C22 65K05 90C51
We are very grateful to André Tits for careful reading of the manuscript, many suggestions, and insightful comments that helped shape the choice of active and inactive blocks, to Florian Potra for helpful discussions, and to anonymous referees for very careful reading and helpful suggestions.
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