求解凸规划问题的一种新的不精确内邻近点方法

A New Inexact Interior Proximal Point Algorithm for Solving Convex Programs

用对数二次邻近点项替代常用的二次邻近点项,导出一种新的不精确内邻近点算法(IIP).讨论了该算法解的存在性,并在某些条件下证明了它的整体收敛性.

In this paper, we present a new inexact proximal point method, where the usual proximal quadratic term is replaced by a logarithmic-quadratic proximal term, and lead to an inexact interior proximal point algorithm(IIP). We first give an existence result for the solution of (IIP). Under some mild assumptions, we also prove that this new algorithm is globally convergent.