Zobrazeno 1 - 10
of 151
pro vyhledávání: '"Kruger, A. Y."'
In the paper, we extend the widely used in optimization theory decoupling techniques to infinite collections of functions. Extended concepts of uniform lower semicontinuity and firm uniform lower semicontinuity as well as the new concepts of weak uni
Externí odkaz:
http://arxiv.org/abs/2409.00573
The paper explores a new extremality model involving collections of arbitrary families of sets. We demonstrate its applicability to set-valued optimization problems with general preferences, weakening the assumptions of the known results and streamli
Externí odkaz:
http://arxiv.org/abs/2407.20473
Publikováno v:
Optimization, 2024
The paper proposes another extension of the extremal principle. A new extremality model involving collections of arbitrary families of sets is studied. It generalizes the conventional model based on linear translations of given sets as well as its se
Externí odkaz:
http://arxiv.org/abs/2403.16511
Publikováno v:
J. Math.Anal.Appl. 532 (2024) 127985
We revisit the decoupling approach widely used (often intuitively) in nonlinear analysis and optimization and initially formalized about a quarter of a century ago by Borwein & Zhu, Borwein & Ioffe and Lassonde. It allows one to streamline proofs of
Externí odkaz:
http://arxiv.org/abs/2305.08484
Autor:
Gfrerer, Helmut, Kruger, Alexander Y.
The paper extends the 2003 radius of metric regularity theorem by Dontchev, Lewis & Rockafellar by providing an exact formula for the radius with respect to Lipschitz continuous perturbations in general Asplund spaces, thus, answering affirmatively a
Externí odkaz:
http://arxiv.org/abs/2210.13790
Autor:
Gfrerer, Helmut, Kruger, Alexander Y.
Publikováno v:
Computational Optimization and Applications (2023)
The paper continues our previous work [7] on the radius of subregularity that was initiated by Asen Dontchev. We extend the results of [7] to general Banach/Asplund spaces and to other classes of perturbations, and sharpen the coderivative tools used
Externí odkaz:
http://arxiv.org/abs/2206.10347
Autor:
Kruger, Alexander Y., Mehlitz, Patrick
Approximate necessary optimality conditions in terms of Fr\'echet subgradients and normals for a rather general optimization problem with a potentially non-Lipschitzian objective function are established with the aid of Ekeland's variational principl
Externí odkaz:
http://arxiv.org/abs/2110.07268
Publikováno v:
Set-Valued and Variational Analysis (2022) 30:1423-1441
The paper utilizes H\"older graphical derivatives for characterizing H\"older strong subregularity, isolated calmness and sharp minimum. As applications, we characterize H\"older isolated calmness in linear semi-infinite optimization and H\"older sha
Externí odkaz:
http://arxiv.org/abs/2106.08149
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 April 2024 532(2)
Publikováno v:
Optimization (2022) 71:4, 1021-1053
We propose a unifying general framework of quantitative primal and dual sufficient and necessary error bound conditions covering linear and nonlinear, local and global settings. The function is not assumed to possess any particular structure apart fr
Externí odkaz:
http://arxiv.org/abs/2012.03941