Information Geometry and Primal-Dual Interior-point Algorithms

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

An Information Geometric Approach to Polynomial-time Interior-point Algorithms: Complexity Bound via Curvature Integral

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