Generalized quadratic augmented Lagrangian methods with nonmonotone penalty parameters (Q442809)

Summary: For the nonconvex optimization problem with both equality and inequality constraints, we introduce a new augmented Lagrangian function and propose the corresponding multiplier algorithm. A new iterative strategy on the penalty parameter is presented. Different global convergence properties are established depending on whether the penalty parameter is bounded. Even if the iterative sequence \(\{x^k\}\) 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.