Iterative algorithm for solving a class of convex feasibility problem

作     者：Li, Chunmei Duan, Xuefeng Lu, Linzhang Wang, Qingwen Shen, Shuqian 

作者机构：Guizhou Normal Univ Sch Math Sci Guiyang 550001 Guizhou Peoples R China Guilin Univ Elect Technol Coll Math & Computat Sci Guangxi Key Lab Cryptog & Informat Secur Key Lab Data Anal & ComputatGuangxi Coll & Univ Guilin 541004 Peoples R China Shanghai Univ Dept Math Shanghai 200444 Peoples R China China Univ Petr Coll Sci Qingdao 257061 Peoples R China 

出 版 物：《JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS》 (计算与应用数学杂志)

年 卷 期：2019年第352卷

页      面：352-367页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Natural Science Foundation of China [11561015, 11671105, 11761024] Natural Science Foundation of Guangxi Province [2016GXNSFFA380009, 2017GXNSFBA198082, 2016GXNSFAA380074] Guangxi Key Laboratory of Cryptography and Information Security, China [GCIS201616] talent program of Guilin University of Electronic Technology, China 

主　　题：Convex feasibility problem Projection formula Relaxed alternating projection algorithm Quantum computation 

摘      要：In this paper, we consider a class of convex feasibility problem, which arises in quantum computation. Based on the matrix equation theory, the feasible sets are characterized by exploiting the special structure of the linear constraints, and its analytic expression is given. By making use of the nice structure properties and the KKT condition, we derive the projection formulas of a matrix onto the feasible sets. The relaxed alternating projection method is designed to solve the convex feasibility problem. Numerical experiments show that the new method is feasible and effective. (C) 2018 Elsevier B.V. All rights reserved.