Superlinear Convergence of Interior-Point Algorithms for Semidefinite Programming

F. A. Potra and R. Sheng
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F. A. Potra: University of Iowa
R. Sheng: Argonne National Laboratory

Journal of Optimization Theory and Applications, 1998, vol. 99, issue 1, No 6, 103-119

Abstract: Abstract We prove the superlinear convergence of the primal-dual infeasible interior-point path-following algorithm proposed recently by Kojima, Shida, and Shindoh and by the present authors, under two conditions: (i) the semidefinite programming problem has a strictly complementary solution; (ii) the size of the central path neighborhood approaches zero. The nondegeneracy condition suggested by Kojima, Shida, and Shindoh is not used in our analysis. Our result implies that the modified algorithm of Kojima, Shida, and Shindoh, which enforces condition (ii) by using additional corrector steps, has superlinear convergence under the standard assumption of strict complementarity. Finally, we point out that condition (ii) can be made weaker and show the superlinear convergence under the strict complementarity assumption and a weaker condition than (ii).

Keywords: Semidefinite programming; path-following algorithms; infeasible interior-point algorithms; polynomiality; superlinear convergence (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1021700210959

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