Generalized Quadratic Augmented Lagrangian Methods with Nonmonotone Penalty Parameters - Xunzhi Zhu; Jinchuan Zhou; Lili Pan; Wenling Zhao (Journal of Applied Mathematics)
For nonconvex optimization problem with both equality and inequality constraints, we introduce a new augmented Lagrangian function and propose the corresponding multiplier algorithm. New iterative strategy on penalty parameter is presented. Different global convergence properties are established depending on whether the penalty parameter is bounded. Even if the iterative sequence 𝑥𝑘 is divergent, we present a necessary and sufficient condition for the convergence of {𝑓(𝑥𝑘)} to the optimal value. Finally, preliminary numerical experience is reported.