Mathematical programming for the sum of two convex functions with applications to lasso problem, split feasibility problems, and image deblurring problem

Fixexd point theory and applications

Chih Sheng Chuang¹  Zenn-Tsun Yu²  Lai-Jiu Lin³ 

[1] Department of Applied Mathematics, National Sun Yat Sen University, Kaohsiung, Taiwan;Department of Electronic Engineering, Nan Kai University of Technology, Nantou, Taiwan;Department of Mathematics, National Changhua University of Education, Changhua, Taiwan

关键词: lasso problem;    mathematical programming for the sum of two functions;    split feasibility problem;    gradient-projection algorithm;    proximal point algorithm;    90C33;    90C34;    90C59;   

DOI  :  10.1186/s13663-015-0388-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, two iteration processes are used to find the solutions of the mathematical programming for the sum of two convex functions. In infinite Hilbert space, we establish two strong convergence theorems as regards this problem. As applications of our results, we give strong convergence theorems as regards the split feasibility problem with modified CQ method, strong convergence theorem as regards the lasso problem, and strong convergence theorems for the mathematical programming with a modified proximal point algorithm and a modified gradient-projection method in the infinite dimensional Hilbert space. We also apply our result on the lasso problem to the image deblurring problem. Some numerical examples are given to demonstrate our results. The main result of this paper entails a unified study of many types of optimization problems. Our algorithms to solve these problems are different from any results in the literature. Some results of this paper are original and some results of this paper improve, extend, and unify comparable results in existence in the literature.

【 授权许可】

CC BY