Splitting augmented Lagrangian method for optimization problems with a cardinality constraint and semicontinuous variables. (2nd September 2016)

• Record Type: Journal Article
• Authors: Bai, Yanqin; Liang, Renli; Yang, Zhouwang
• Is Part Of: Optimization methods and software. Volume 31:Number 5(2016)
• Page Start: 1089
• Page End: 1109
• Publication Date: 2016-09-02
• Subjects: cardinality constraint and semicontinuous variables optimization problem -- alternating direction method of multipliers -- augmented Lagrangian decomposition; 90C11 -- 90C27 -- 90C30; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2016.1196206
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : We propose a new splitting augmented Lagrangian method (SALM) for solving a class of optimization problems with both cardinality constraint and semicontinuous variables constraint. The proposed approach, inspired by the penalty decomposition method in [Z.S. Lu and Y. Zhang, Sparse approximation via penalty decomposition methods, SIAM J. Optim. 23(4) (2013), pp. 2448–2478], splits the problem into two subproblems using auxiliary variables. SALM solves two subproblems alternatively. Furthermore, we prove the convergence of SALM, under certain assumptions. Finally, SALM is implemented on the portfolio selection problem and the compressed sensing problem, respectively. Numerical results show that SALM outperforms the well-known tailored approach in CPLEX 12.6 and the penalty decomposition method, respectively.