Title: Error bounds for conic feasibility problems: case studies on the exponential cone
|Ting Kei Pong
|The Hong Kong Polytechnic University
Abstract: Conic feasibility problems naturally arise from linear conic programming problems. An understanding of error bounds for these problems is instrumental in the design of termination criteria for conic solvers and the study of convergence rate of algorithms. In this talk, we will present a general framework for deriving error bounds for conic feasibility problems. Our framework is based on facial reduction and a new object called one-step facial residual function. We develop tools to compute these facial residual functions, which are applicable even when the projections onto the cones under study are not easy to analyze. We illustrate how our framework can be applied to obtain error bounds for the exponential cone.
This is joint work with Scott B. Lindstrom and Bruno F. Lourenço.