Proximal-like algorithm using the quasi D-function for convex second-order cone programming

In this paper, we present a measure of distance in second-order cone based on a class of continuously differentiable strictly convex function on IR++. Since the distance function has some favorable properties similar to those of D-function [8], we here refer it as a quasi D-function. Then, a proximal-like algorithm using the quasi D-function is proposed and applied to the second-cone programming problem which is to minimize a closed proper convex function with general second-order cone constraints. Like the proximal point algorithm using D-function [5, 8], we under some mild assumptions establish the global convergence of the algorithm expressed in terms of function values, and show that the sequence generated by the proposed algorithm is bounded and every accumulation point is a solution to the considered problem.