Split proximal linearized algorithm and convergence theorems for the split DC program

Chih-Sheng Chuang,Chi-Ming Chen

doi:10.1186/s13660-019-2084-9

Abstract

In this paper, we study the split DC program by using the split proximal linearized algorithm. Further, linear convergence theorem for the proposed algorithm is established under suitable conditions. As applications, we first study the DC program (DCP). Finally, we give numerical results for the proposed convergence results.

Highlights

We recall the minimization problem for convex functions: Find x ∈ arg min f (x) : x ∈ H, (MP1)where H is a real Hilbert space and f : H →
Showed that {xn}n∈N converges weakly to a minimizer of f under suitable conditions. This algorithm is useful, only for convex problems, because the idea for this algorithm is based on the monotonicity of subdifferential operators of convex functions
It is important to consider the relation between nonconvex problems and a proximal point algorithm

Summary

Introduction

We recall the minimization problem for convex functions: Find x ∈ arg min f (x) : x ∈ H , (MP1)where H is a real Hilbert space and f : H → Algorithm 1.1 (Proximal point algorithm for (DCP) [16]) Let {βn}n∈N be a sequence in (0, ∞), and let g, h : Rk → R be proper lower semicontinuous and convex functions.

Results

Conclusion