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

Abstract EN

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 Gu¨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 O1/k2.