Zobrazeno 1 - 10
of 56
pro vyhledávání: '"Benko, Matúš"'
Autor:
Benko, Matúš, Mehlitz, Patrick
As a starting point of our research, we show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationar
Externí odkaz:
http://arxiv.org/abs/2402.16530
Autor:
Benko, Matúš, Mehlitz, Patrick
In this paper, we characterize Lipschitzian properties of different multiplier-free and multiplier-dependent perturbation mappings associated with the stationarity system of a so-called generalized nonlinear program popularized by Rockafellar. Specia
Externí odkaz:
http://arxiv.org/abs/2401.08163
Autor:
Benko, Matus, Rockafellar, R. Tyrrell
Much is known about when a locally optimal solution depends in a single-valued Lipschitz continuous way on the problem's parameters, including tilt perturbations. Much less is known, however, about when that solution and a uniquely determined multipl
Externí odkaz:
http://arxiv.org/abs/2401.00601
Autor:
Benko, Matúš, Mehlitz, Patrick
In this paper, we readdress the classical topic of second-order sufficient optimality conditions for optimization problems with nonsmooth structure. Based on the so-called second subderivative of the objective function and of the indicator function a
Externí odkaz:
http://arxiv.org/abs/2206.03918
Autor:
Benko, Matúš, Mehlitz, Patrick
During the last years, asymptotic (or sequential) constraint qualifications, which postulate upper semicontinuity of certain set-valued mappings and provide a natural companion of asymptotic stationarity conditions, have been shown to be comparativel
Externí odkaz:
http://arxiv.org/abs/2205.00775
Autor:
Benko, Matúš, Mehlitz, Patrick
We show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order $1$), satisfies stationa
Externí odkaz:
http://arxiv.org/abs/2204.13932
In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs.Unlike the existing results in the literature, our conditions pro
Externí odkaz:
http://arxiv.org/abs/2203.10015
Autor:
Benko, Matúš, Mehlitz, Patrick
Publikováno v:
Journal of Nonsmooth Analysis and Optimization, Volume 2, Original research articles (August 6, 2021) jnsao:7215
Implicit variables of a mathematical program are variables which do not need to be optimized but are used to model feasibility conditions. They frequently appear in several different problem classes of optimization theory comprising bilevel programmi
Externí odkaz:
http://arxiv.org/abs/2008.08677
Autor:
Benko, Matúš, Mehlitz, Patrick
We establish two types of estimates for generalized derivatives of set-valued mappings which carry the essence of two basic patterns observed troughout the pile of calculus rules. These estimates also illustrate the role of the essential assumptions
Externí odkaz:
http://arxiv.org/abs/2008.07114
Autor:
Benko, Matúš
Publikováno v:
Journal of Nonsmooth Analysis and Optimization, Volume 2, Original research articles (June 26, 2021) jnsao:5881
In this paper, we study continuity and Lipschitzian properties of set-valued mappings, focusing on inner-type conditions. We introduce new notions of inner calmness* and, its relaxation, fuzzy inner calmness*. We show that polyhedral maps enjoy inner
Externí odkaz:
http://arxiv.org/abs/1910.13309