Local convergence analysis of a primal-dual method for nonlinear programming without constraint qualification

par Tran Ngoc Nguyen

vendredi 5 oct. 2018, 11:30 → 12:30 Europe/Paris

XLIM Salle X.203

In nonlinear optimization, the lack of the Mangasarian-Fromovitz constraint qualification (MFCQ) may lead to numerical difficulties and in particular to slow down the convergence of an optimization algorithm. In this talk we analyse the local behavior of an algorithm based on a mixed logarithmic barrier-augmented Lagrangian method for solving a nonlinear optimization problem. This work has been motivated by the good efficiency and robustness of this algorithm, even in the degenerate case in which MFCQ does not hold. Furthermore, we detail different updating rules of the parameters of the algorithm to obtain a rapid (superlinear or quadratic) rate of convergence of the sequence of iterates. The local convergence analysis is done by using a stability theorem of Hager and Gowda, as well as a property of uniform boundedness of the inverse of the regularized Jacobian matrix used in the primal-dual method. Numerical results on degenerate problems are also presented.