A Constraint-Reduced Algorithm for Semidefinite Optimization Problems with Superlinear Convergence

Sungwoo Park (swpark81gmail.com)

Abstract: Constraint reduction is an essential method because the computational cost of the interior point methods can be effectively saved. Park and O'Leary proposed a constraint-reduced predictor-corrector algorithm for semidefinite programming with polynomial global convergence, but they did not show its superlinear convergence. We first develop a constraint-reduced algorithm for semidefinite programming having both polynomial global and superlinear local convergences. The new algorithm repeats a corrector step to have an iterate tangentially approach a central path, by which superlinear convergence can be achieved.

Keywords: Semidefinite programming, Interior point methods, Constraint reduction, Primal dual infeasible, Local convergence

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

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Entry Submitted: 05/21/2015
Entry Accepted: 05/22/2015
Entry Last Modified: 02/14/2016

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