iteration complexities – Optimization Online

Curvature Integrals and Iteration Complexities in SDP and Symmetric Cone Programs

Published: 2011/09/30

Linear, Cone and Semidefinite Programming curvature, interior point methods, iteration complexities, path-following methods, primal-dual algorithms, semidefinite programming, symmetric cones

In this paper, we study iteration complexities of Mizuno-Todd-Ye predictor-corrector (MTY-PC) algorithms in SDP and symmetric cone programs by way of curvature integrals. The curvature integral is defined along the central path, reflecting the geometric structure of the central path. The idea to exploit the curvature of the central path for the analysis of iteration … Read more

Information Geometry and Interior-Point Algorithms in SDP and Symmetric Cone Programs

Published: 2011/09/30, Updated: 2011/10/10

Satoshi Kakihara

Atsumi Ohara

Takashi Tsuchiya

Linear, Cone and Semidefinite Programming curvature integral, information geometry, interior point methods, iteration complexities, primal-dual algorithms, semidefinite programming, symmetric cones

This paper is a continuation of the paper Kakihara, Ohara and Tsuchiya by the authors where they demonstrated that the number of iterations of Mizuno-Todd-Ye predictor-corrector primal-dual interior-point methods for SDP and more generally symmetric cone programs is (asymptotically) expressed with an integral over the central trajectory called “curvature integral.” It was shown that the … Read more