Artículos de revistas
Evaluation Complexity For Nonlinear Constrained Optimization Using Unscaled Kkt Conditions And High-order Models
Registro en:
Siam Journal On Optimization. Siam Publications, v. 26, p. 951 - 967, 2016.
1052-6234
1095-7189
WOS:000386453800003
10.1137/15M1031631
Autor
Birgin
E. G.; Gardenghi
J. L.; Martinez
J. M.; Santos
S. A.; Toint
Ph. L.
Institución
Resumen
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) The evaluation complexity of general nonlinear, possibly nonconvex, constrained optimization is analyzed. It is shown that, under suitable smoothness conditions, an epsilon-approximate first-order critical point of the problem can be computed in order O(epsilon(1-2(p+1)/p)) evaluations of the problem's functions and their first p derivatives. This is achieved by using a two-phase algorithm inspired by Cartis, Gould, and Toint [SIAM J. Optim., 21 (2011), pp. 1721-1739; SIAM J. Optim., 23 (2013), pp. 1553-1574]. It is also shown that strong guarantees (in terms of handling degeneracies) on the possible limit points of the sequence of iterates generated by this algorithm can be obtained at the cost of increased complexity. At variance with previous results, the epsilon-approximate first-order criticality is defined by satisfying a version of the KKT conditions with an accuracy that does not depend on the size of the Lagrange multipliers. 26 2 951 967 Brazilian agency FAPESP [2010/10133-0, 2013/03447-6, 2013/05475-7, 2013/07375-0, 2013/23494-9] Brazilian agency CNPq [304032/2010-7, 309517/2014-1, 303750/2014-6, 490326/2013-7] Belgian National Fund for Scientific Research (FNRS) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)