Global convergence of modified augmented Lagrangian methods for nonlinear semidefinite programming

• Published in: Computational optimization and applications Vol. 56; no. 3; pp. 531 - 558
• Main Authors: Wu, Huixian, Luo, Hezhi, Ding, Xiaodong, Chen, Guanting
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.12.2013; Springer Nature B.V
• Subjects: Algorithms; Computational mathematics; Convex and Discrete Geometry; Eigenvalues; Lagrange multiplier; Management Science; Mathematical models; Mathematics; Mathematics and Statistics; Methods; Nonlinear equations; Nonlinear programming; Operations Research; Operations Research/Decision Theory; Optimization; Quadratic programming; Science; Semidefinite programming; Statistics; Studies; Theorems; Modified augmented Lagrangian methods; Boundedness of multipliers; Convergence to KKT points; Nonlinear semidefinite program
• ISSN: 0926-6003; 1573-2894
• DOI: 10.1007/s10589-013-9568-1

We investigate in this paper global convergence properties of the augmented Lagrangian method for nonlinear semidefinite programming (NLSDP). Four modified augmented Lagrangian methods for solving NLSDP based on different algorithmic strategies are proposed. Possibly infeasible limit points of the proposed methods are characterized. It is proved that feasible limit points that satisfy the Mangasarian-Fromovitz constraint qualification are KKT points of NLSDP without requiring the boundedness condition of the multipliers. Preliminary numerical results are reported to compare the performance of the modified augmented Lagrangian methods.