A dual-primal balanced augmented Lagrangian method for linearly constrained convex programming

Xu, Shengjie1,2

2022-08-01

10.1007/s12190-022-01779-y

Journal of Applied Mathematics and Computing   影响因子和分区

1598-5865

1865-2085

Most recently, a balanced augmented Lagrangian method (ALM) has been proposed by He and Yuan for the canonical convex minimization problem with linear constraints, which advances the original ALM by balancing its subproblems, improving its implementation and enlarging its applicable range. In this paper, we propose a dual-primal version of the newly developed balanced ALM, which updates the new iterate via a conversely dual-primal iterative order formally. The new algorithm inherits all advantages of the prototype balanced ALM, and it can be extended to more general separable convex programming problems with both linear equality and inequality constraints. The convergence analysis of the proposed method can be well conducted in the context of variational inequalities. In particular, by some application problems, we numerically validate that these balanced ALM type methods can outperform existing algorithms of the same kind significantly.

Augmented Lagrangian method Convex programming Dual-primal Proximal point algorithm Variational inequality

SCI ; EI

英语

通讯

Mathematics

Mathematics, Applied ; Mathematics

WOS:000842873300002

SPRINGER HEIDELBERG

20223512641178

Constrained optimization ; Iterative methods ; Lagrange multipliers ; Software prototyping ; Variational techniques

Computer Programming:723.1 ; Calculus:921.2 ; Numerical Methods:921.6 ; Systems Science:961

Web of Science

1.Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
2.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China

Xu, Shengjie. A dual-primal balanced augmented Lagrangian method for linearly constrained convex programming[J]. Journal of Applied Mathematics and Computing,2022,69(1):1015-1035.

Xu, Shengjie.(2022).A dual-primal balanced augmented Lagrangian method for linearly constrained convex programming.Journal of Applied Mathematics and Computing,69(1),1015-1035.

Xu, Shengjie."A dual-primal balanced augmented Lagrangian method for linearly constrained convex programming".Journal of Applied Mathematics and Computing 69.1(2022):1015-1035.