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Journal of Optimization Theory and Applications

, Volume 166, Issue 2, pp 558–571 | Cite as

A Polynomial Time Constraint-Reduced Algorithm for Semidefinite Optimization Problems

  • Sungwoo ParkEmail author
  • Dianne P. O’Leary
Article

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 

Mathematics Subject Classification

90C22 65K05 90C51 

Notes

Acknowledgments

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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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.KCG holdingsJersey CityUSA
  2. 2.Computer Science Department and Institute for Advanced Computer StudiesUniversity of MarylandCollege ParkUSA

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