3 papers
math.FA2025
Generalized Separation of Collections of Sets
Nguyen Duy Cuong, Alexander Y. Kruger
We show that the existing generalized separation statements including the conventional extremal principle and its extensions differ {in the ways norms on product spaces are defined…
math.OC2025
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…
math.OC2025
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…