Computational & Applied Mathematics
On-line version ISSN 1807-0302
DINIZ-EHRHARDT, M. A.; MARTINEZ, J. M. and PEDROSO, L. G.. Derivative-free methods for nonlinear programming with general lower-level constraints. Comput. Appl. Math. [online]. 2011, vol.30, n.1, pp. 19-52. ISSN 1807-0302. http://dx.doi.org/10.1590/S1807-03022011000100003.
Augmented Lagrangian methods for derivative-free continuous optimization with constraints are introduced in this paper. The algorithms inherit the convergence results obtained by Andreani, Birgin, Martínez and Schuverdt for the case in which analytic derivatives exist and are available. In particular, feasible limit points satisfy KKT conditions under the Constant Positive Linear Dependence (CPLD) constraint qualification. The form of our main algorithm allows us to employ well established derivative-free subalgorithms for solving lower-level constrained subproblems. Numerical experiments are presented.
Keywords : nonlinear programming; Augmented Lagrangian; global convergence; optimality conditions; derivative-free optimization; constraint qualifications.