Generalized Quadratic Augmented Lagrangian Methods with Nonmonotone Penalty Parameters

Abstract

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 $\left\{x^k\right\}$ is divergent, we present a necessary and sufficient condition for the convergence of $\{f(x^k)\}$ to the optimal value. Finally, preliminary numerical experience is reported.