Efficient projected gradient methods for cardinality constrained optimization

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（2）
• 页码范围: 245-268
• 页数: 24页
• 语种: 英文

摘要

Sparse optimization has attracted increasing attention in numerous areas such as compressed sens ing,financial optimization and image processing.In this paper,we first consider a special class of cardinality constrained optimization problems,which involves box constraints and a singly linear constraint.An efficient approach is provided for calculating the projection over the feasibility set after a careful analysis on the projection subproblem.Then we present several types of projected gradient methods for a general class of cardinality constrained optimization problems.Global convergence of the methods is established under suitable assumptions.Finally,we illustrate some applications of the proposed methods for signal recovery and index tracking.Especially for index tracking,we propose a new model subject to an adaptive upper bound on the sparse portfolio weights.The computational results demonstrate that the proposed projected gradient methods are efficient in terms of solution quality.