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

Sungwoo Park ()
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Sungwoo Park: KCG Holdings

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 2, No 10, 512-527

Abstract: 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. This study proves its convergence rate and shows its effective cost saving in numerical experiments.

Keywords: Semidefinite programming; Interior point methods; Constraint reduction; Primal dual infeasible; Local convergence; 90C22; 65K05; 90C51 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-016-0917-y

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