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Superlinear Convergence of
Interior-Point Algorithms for Semidefinite Programming

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Florian A. Potra and Rongqin Sheng

We prove the superlinear convergence of the primal-dual
infeasible-interior-point path-following
algorithm proposed recently by Kojima, Shida and Shindoh and
the present authors, under two conditions: (1) the
SDP problem has a strictly complementary solution, and (2) 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 (2) by using
additional corrector steps, has superlinear convergence under
the standard assumption of strict complementarity.
Reports On Computational Mathematics, No. 86/1996,
Department Of Mathematics, The University Of Iowa.