Nonuniqueness of Solutions of a Class of0-minimization Problems  

作　　者：Jia-Liang Xu 

机构地区：[1]Hua Loo-Keng Center for Mathematical Sciences,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Journal of the Operations Research Society of China》2021年第4期893-908,共16页中国运筹学会会刊（英文）

摘　　要：Recently,finding the sparsest solution of an underdetermined linear system has become an important request in many areas such as compressed sensing,image processing,statistical learning,and data sparse approximation.In this paper,we study some theoretical properties of the solutions to a general class of0-minimization problems,which can be used to deal with many practical applications.We establish some necessary conditions for a point being the sparsest solution to this class of problems,and we also characterize the conditions for the multiplicity of the sparsest solutions to the problem.Finally,we discuss certain conditions for the boundedness of the solution set of this class of problems.

关 键 词：0-minimization SPARSITY NONUNIQUENESS BOUNDEDNESS 

分 类 号：O17[理学—数学]