83 citations · 490 across the 30 of their papers we have counts for
31 papers
Fuzzy multiplier, sum and intersection rules in non-Lipschitzian settings: decoupling approach revisited
Marián Fabian, Alexander Y. Kruger, Patrick Mehlitz
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…
The Radius of Metric Regularity Revisited
Helmut Gfrerer, Alexander Y. Kruger
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 pe…
Radius Theorems for Subregularity in Infinite Dimensions
Helmut Gfrerer, Alexander Y. Kruger
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 o…
Optimality conditions, approximate stationarity, and applications -- a story beyond Lipschitzness
Alexander Y. Kruger, Patrick Mehlitz
Approximate necessary optimality conditions in terms of Fréchet subgradients and normals for a rather general optimization problem with a potentially non-Lipschitzian objective fun…
Isolated calmness and sharp minima via Hölder graphical derivatives
Alexander Y. Kruger, Marco A. López, Xiaoqi Yang +1
The paper utilizes Hölder graphical derivatives for characterizing Hölder strong subregularity, isolated calmness and sharp minimum. As applications, we characterize Hölder isolate…
Error bounds revisited
Nguyen Duy Cuong, Alexander Y. Kruger
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. Th…
Uniform Regularity of Set-Valued Mappings and Stability of Implicit Multifunctions
Nguyen Duy Cuong, Alexander Y. Kruger
We propose a unifying general (i.e. not assuming the mapping to have any particular structure) view on the theory of regularity and clarify the relationships between the existing p…
Zero Duality Gap in View of Abstract Convexity
Hoa T. Bui, Regina S. Burachik, Alexander Y. Kruger +1
Using tools provided by the theory of abstract convexity, we extend conditions for zero duality gap to the context of nonconvex and nonsmooth optimization. Mimicking the classical…
Necessary Conditions for Non-Intersection of Collections of Sets
Hoa T. Bui, Alexander Y. Kruger
This paper continues studies of non-intersection properties of finite collections of sets initiated 40 years ago by the extremal principle. We study elementary non-intersection pro…
Transversality Properties: Primal Sufficient Conditions
Nguyen Duy Cuong, Alexander Y. Kruger
The paper studies 'good arrangements' (transversality properties) of collections of sets in a normed vector space near a given point in their intersection. We target primal (metric…
Extremality, Stationarity and Generalized Separation of Collections of Sets
Hoa T. Bui, Alexander Y. Kruger
The core arguments used in various proofs of the extremal principle and its extensions as well as in primal and dual characterizations of approximate stationarity and transversalit…
The Radius of Metric Subregularity
Asen L. Dontchev, Helmut Gfrerer, Alexander Y. Kruger +1
There is a basic paradigm, called here the radius of well-posedness, which quantifies the "distance" from a given well-posed problem to the set of ill-posed problems of the same ki…
Hölder Error Bounds and Hölder Calmness with Applications to Convex Semi-Infinite Optimization
Alexander Kruger, Marco López, Xiaoqi Yang +1
Using techniques of variational analysis, necessary and sufficient subdifferential conditions for Hölder error bounds are investigated and some new estimates for the corresponding…
On semiregularity of mappings
R. Cibulka, M. Fabian, A. Y. Kruger
There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting proper…
About Extensions of the Extremal Principle
Hoa T. Bui, Alexander Y. Kruger
In this article, after recalling and discussing the conventional extremality, local extremality, stationarity and approximate stationarity properties of collections of sets and the…
Strong Metric Subregularity of Mappings in Variational Analysis and Optimization
Radek Cibulka, Asen Dontchev, Alexander Kruger
Although the property of strong metric subregularity of set-valued mappings has been present in the literature under various names and with various definitions for more than two de…
About intrinsic transversality of pairs of sets
Alexander Y. Kruger
The article continues the study of the 'regular' arrangement of a collection of sets near a point in their intersection. Such regular intersection or, in other words, transversalit…
About subtransversality of collections of sets
Alexander Y. Kruger, D. Russell Luke, Nguyen H. Thao
We provide dual sufficient conditions for subtransversality of collections of sets in an Asplund space setting. For the convex case, we formulate a necessary and sufficient dual cr…
Set Regularities and Feasibility Problems
Alexander Y. Kruger, D. Russell Luke, Nguyen H. Thao
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent fea…
Perturbation of error bounds
A. Y. Kruger, M. A. López, M. A. Théra
Our aim in the current article is to extend the developments in Kruger, Ngai & Théra, SIAM J. Optim. 20(6), 3280-3296 (2010) and, more precisely, to characterize, in the Banach spa…
Borwein-Preiss Vector Variational Principle
Alexander Y. Kruger, Somyot Plubtieng, Thidaporn Seangwattana
This article extends to the vector setting the results of our previous work Kruger et al. (2015) which refined and slightly strengthened the metric space version of the Borwein-Pre…
Borwein-Preiss Variational Principle Revisited
A. Y. Kruger, S. Plubtieng, T. Seangwattana
In this article, we refine and slightly strengthen the metric space version of the Borwein-Preiss variational principle due to Li, Shi, J. Math. Anal. Appl. 246, 308-319 (2000), cl…
Nonlinear Metric Subregularity
Alexander Y. Kruger
In this article, we investigate nonlinear metric subregularity properties of set-valued mappings between general metric or Banach spaces. We demonstrate that these properties can b…
Regularity of collections of sets and convergence of inexact alternating projections
Alexander Y. Kruger, Nguyen H. Thao
We study the usage of regularity properties of collections of sets in convergence analysis of alternating projection methods for solving feasibility problems. Several equivalent ch…