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Splitting augmented Lagrangian method for optimization problems with a cardinality constraint and semicontinuous variables. (English) Zbl 1355.90053

Summary: 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. Lu and Y. Zhang, SIAM J. Optim. 23, No. 4, 2448–2478 (2013; Zbl 1295.90056)], 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.

MSC:

90C11 Mixed integer programming
90C27 Combinatorial optimization
90C30 Nonlinear programming

Citations:

Zbl 1295.90056

Software:

CPLEX
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Full Text: DOI

References:

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