Atsumi Ohara 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
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
In this paper, we study polynomial-time interior-point algorithms in view of information geometry. We introduce an information geometric structure for a conic linear program based on a self-concordant barrier function. Riemannian metric is defined with the Hessian of the barrier function. We introduce two connections $\nabla$ and $\nabla^*$ which roughly corresponds to the primal and … Read more
In this paper, we study polynomial-time interior-point algorithms in view of information geometry. Information geometry is a differential geometric framework which has been successfully applied to statistics, learning theory, signal processing etc. We consider information geometric structure for conic linear programs introduced by self-concordant barrier functions, and develop a precise iteration-complexity estimate of the polynomial-time … Read more