Local behavior of an augmented Lagrangian method for degenerate nonlinear programming

DAMIÁN FERNÁNDEZ; MIKHAIL SOLODOV

Santiago, Chile

Conferencia; The International Conference on Continuous Optimization (ICCOPT); 2010

It is known that when the penalty parameter is very large, the subproblem associated with the minimization of the augmented Lagrangian may be very difficult. The necessity of maintaining bounded penalty parameter is controversial, because ill-conditioning disappears with a suitable decomposition of the subproblem. In this work we propose that the penalty parameter should take values inversely proportional to an error bound function associated to the KKT system. We obtain local quadratic convergence for both, primal and primal-dual sequence, taking into account possible degeneracy of the constraints.