A globally convergent sSQP method

DAMIÁN FERNÁNDEZ; ELVIO A. PILOTTA; GERMÁN A. TORRES

Valparaíso

Workshop; III Latin American Workshop on Optimization and Control; 2012

Universidad Técnica Federico Santa María

It is know that the stabilized Sequential Quadratic Programming (sSQP)method has a good local behavior [3], but there are no globally convergent results for this method. In this work we develop a hybrid method that combines Inexact Restoration (IR) [5, 4] andAugmented Lagrangian (AL) [2, 1] methods. In one hand, feasibility of a suitable stabilized subproblem allows us to avoid the restoration phase in the IR method. Therefore,subproblems can be solved efficiently by IR. In the other hand, since the sSQP method is equivalent to a perturbed augmented Lagrangian method, we obtain the same global convergence properties of the augmented Lagrangian method.[1]  R. Andreani, E. G. Birgin, J. M. Martínez and M. L. Schuverdt, Augmented Lagrangian methods under the constant positive linear dependence constraint qualification, Math. Program. , 111 (1-2, Ser. B), pp. 5-32 (2008).[2] A. R. Conn, N. Gould, A. Sartenaer and P. L. Toint, Convergence properties of an augmented Lagrangian algorithm for optimization with a combination of general equality and linear constraints, SIAM J. Optim., 6 (3), 674-703 (1996).[3] D. Fernández and M. Solodov, Stabilized sequential quadratic programming for optimization and a stabilized Newton-type method for variational problems, Math. Program., 125 (1, Ser. A), 47-73 (2010).[4] A. Fischer and A. Friedlander, A new line search inexact restoration approach for nonlinear programming, Comput. Optim. Appl., 46 (2), 333-346 (2010).[5] J. M. Martínez and E. A. Pilotta, Inexact-restoration algorithm for constrained optimization, J. Optim. Theory Appl., 104 (1), 135-163 (2000).