A Polynomial Time Constraint-Reduced Algorithm for Semidefinite Optimization Problems

Sungwoo Park () and Dianne P. O’Leary ()
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Sungwoo Park: KCG holdings
Dianne P. O’Leary: University of Maryland

Journal of Optimization Theory and Applications, 2015, vol. 166, issue 2, No 10, 558-571

Abstract: Abstract 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.

Keywords: Semidefinite programming; Interior point methods; Constraint reduction; Primal dual infeasible; Polynomial complexity; 90C22; 65K05; 90C51 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-015-0714-z

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