Articulo
Extended convergence results for the method of multipliers for nonstrictly binding inequality constraints
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS;
J. Optim. Theory Appl.
Registro en:
0
D92I1028
D92I1028
WOS:A1993MP98500004
0022-3239
Autor
CONTESSE-BECKER, LUIS
Institución
Resumen
In this paper, we extend the classical convergence and rate of convergence results for the method of multipliers for equality constrained problems to general inequality constrained problems, without assuming the strict complementarity hypothesis at the local optimal solution. Instead, we consider an alternative second-order sufficient condition for a strict local minimum, which coincides with the standard one in the case of strict complementary slackness. As a consequence, new stopping rules are derived in order to guarantee a local linear rate of convergence for the method, even if the current Lagrangian is only asymptotically minimized in this more general setting. These extended results allow us to broaden the scope of applicability of the method of multipliers, in order to cover all those problems admitting loosely binding constraints at some optimal solution. This fact is not meaningless, since in practice this kind of problem seems to be more the rule rather than the exception. In proving the different results, we follow the classical primal-dual approach to the method of multipliers, considering the approximate minimizers for the original augmented Lagrangian as the exact solutions for some adequate approximate augmented Lagrangian. In particular, we prove a general uniform continuity property concerning both their primal and their dual optimal solution set maps, a property that could be useful beyond the scope of this paper. This approach leads to very simple proofs of the preliminary results and to a straightforward proof of the main results. 0 11 FONDEF 0 0 2 FONDEF 79