A superlinearly convergent predictor-corrector algorithm for symmetric cone optimization

We discuss and modify the Mizuno-Todd-Ye predictor-corrector interior-point algorithm for symmetric cone optimization problem such that the corrector step is repeated a number of times to keep the iterates sufficiently close to the central path. Then, we establish superlinearconvergence of the modified algorithm under the mere assumption that the problem possesses a strictly complementary optimal solution. Nondegeneracy assumption is not utilized in our analysis. To our knowledge, this is the first demonstration of superlinear convergence for interior-point methods over symmetric cones involving the Jordan algebraic tools.

Keywords:

Symmetric Cone Optimization , Predictor-Corrector Algorithm , Superlinear Convergence