On the Convergence Properties of a Second-Order Augmented Lagrangian Method for Nonlinear Programming Problems with Inequality Constraints

2015 ◽  
Vol 187 (1) ◽  
pp. 248-265 ◽  
Author(s):  
Liang Chen ◽  
Anping Liao
Keyword(s):  
Nonlinear Programming ◽  
Augmented Lagrangian ◽  
Augmented Lagrangian Method ◽  
Inequality Constraints ◽  
Lagrangian Method ◽  
Second Order ◽  
Convergence Properties

scholarly journals New Convergence Properties of the Primal Augmented Lagrangian Method

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Jinchuan Zhou ◽  
Xunzhi Zhu ◽  
Lili Pan ◽  
Wenling Zhao
Keyword(s):  
Optimization Problem ◽  
Augmented Lagrangian ◽  
Augmented Lagrangian Method ◽  
Accumulation Point ◽  
Lagrangian Method ◽  
Iterative Sequence ◽  
Convergence Properties ◽  
Primal Problem ◽  
Kkt Point ◽  
Convergence Results

New convergence properties of the proximal augmented Lagrangian method is established for continuous nonconvex optimization problem with both equality and inequality constrains. In particular, the multiplier sequences are not required to be bounded. Different convergence results are discussed dependent on whether the iterative sequence{xk}generated by algorithm is convergent or divergent. Furthermore, under certain convexity assumption, we show that every accumulation point of{xk}is either a degenerate point or a KKT point of the primal problem. Numerical experiments are presented finally.

Partially Augmented Lagrangian Method for Matrix Inequality Constraints

2004 ◽  
Vol 15 (1) ◽  
pp. 161-184 ◽  
Author(s):  
Dominikus Noll ◽  
Mounir Torki ◽  
Pierre Apkarian
Keyword(s):  
Augmented Lagrangian ◽  
Augmented Lagrangian Method ◽  
Inequality Constraints ◽  
Lagrangian Method ◽  
Matrix Inequality
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