Convergence Analysis on an Accelerated Proximal Point Algorithm for Linearly Constrained Optimization Problems

Abstract

Proximal point algorithm is a type of method widely used in solving optimization problems and some practical problems such as machine learning in recent years. In this paper, a framework of accelerated proximal point algorithm is presented for convex minimization with linear constraints. The algorithm can be seen as an extension to G $\ddot{u}$ ler’s methods for unconstrained optimization and linear programming problems. We prove that the sequence generated by the algorithm converges to a KKT solution of the original problem under appropriate conditions with the convergence rate of $O\left(1/k^2\right)$ .