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12 papers · 1 filter
Sequential Extremal Principle and Necessary Conditions for Minimizing Sequences
Nguyen Duy Cuong, Alexander Y. Kruger
The conventional definition of extremality of a finite collection of sets is extended by replacing a fixed point (extremal point) in the intersection of the sets by a collection of…
Explicit Convergence Rate of The Proximal Point Algorithm under R-Continuity
Ba Khiet Le, Michel Théra
The paper provides a thorough comparison between R-continuity and other fundamental tools in optimization such as metric regularity, metric subregularity and calmness. We show that…
Extremality of families of sets and set-valued optimization
Nguyen Duy Cuong, Alexander Y. Kruger, Nguyen Hieu Thao
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 pr…
Extremality of families of sets
Nguyen Duy Cuong, Alexander Y. Kruger, Nguyen Hieu Thao
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 conventio…
Sliding Mode Observers for Set-valued Lur'e Systems with Uncertainties Beyond Observational Range
Samir Adly, Jun Huang, Ba Khiet Le
In this paper, we introduce a new sliding mode observer for Lur'e set-valued dynamical systems, particularly addressing challenges posed by uncertainties not within the standard ra…
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…