Zobrazeno 1 - 10
of 97
pro vyhledávání: '"Alexey F. Izmailov"'
Publikováno v:
Journal of Optimization Theory and Applications. 196:1008-1035
This work is concerned with conditions ensuring stability of a given solution of a system of nonlinear equations with respect to large (not asymptotically thin) classes of right-hand side perturbations. Our main focus is on those solutions that are i
Autor:
Alexey F. Izmailov
Publikováno v:
Computational Optimization and Applications. 80:943-978
This paper concerns the issue of asymptotic acceptance of the true Hessian and the full step by the sequential quadratic programming algorithm for equality-constrained optimization problems. In order to enforce global convergence, the algorithm is eq
Publikováno v:
Computational Optimization and Applications. 80:587-615
It is well-recognized that in the presence of singular (and in particular nonisolated) solutions of unconstrained or constrained smooth nonlinear equations, the existence of critical solutions has a crucial impact on the behavior of various Newton-ty
Autor:
Mikhail V. Solodov, Alexey F. Izmailov
Publikováno v:
Journal of Optimization Theory and Applications. 193:491-522
We introduce a perturbed augmented Lagrangian method framework, which is a convenient tool for local analyses of convergence and rates of convergence of some modifications of the classical augmented Lagrangian algorithm. One example to which our deve
Publikováno v:
Computational Optimization and Applications. 78:273-286
In the case of singular (and possibly even nonisolated) solutions of nonlinear equations, while superlinear convergence of the Newton method cannot be guaranteed, local linear convergence from large domains of starting points still holds under certai
Publikováno v:
Journal of Optimization Theory and Applications. 185:679-699
This paper answers in the affirmative the long-standing question of nonlinear analysis, concerning the existence of a continuous single-valued local selection of the right inverse to a locally Lipschitzian mapping. Moreover, we develop a much more ge
Publikováno v:
Mathematical Programming. 187:697-721
As is well known, when initialized close to a nonsingular solution of a smooth nonlinear equation, the Newton method converges to this solution superlinearly. Moreover, the common Armijo linesearch procedure used to globalize the process for converge
Autor:
Alexey F. Izmailov, Aram V. Arutyunov
Publikováno v:
SIAM Journal on Optimization. 30:604-629
We study stability properties of a given solution of a constrained equation, where the constraint has the form of the inclusion into an arbitrary closed convex set. We are mostly interested in thos...
Publikováno v:
SIAM Journal on Optimization. 30:1555-1581
It is a well-known phenomenon that the presence of critical Lagrange multipliers in constrained optimization problems may cause a deterioration of the convergence speed of primal-dual Newton-type m...
Publikováno v:
Tambov University Reports. Series: Natural and Technical Sciences. :150-165
Local superlinear convergence of the stabilized sequential quadratic programming method is established under very weak assumptions not involving any constraint qualification conditions. However, all attempts to globalize convergence of this method in