6 papers
Norm Minimisation Problems Involving Distances to Convex Sets
Doan Huu Hieu, Nguyen Duy Cuong
The paper studies product-space norm minimisation problems involving distances to convex sets. Using standard tools from convex and functional analysis, we establish complete dual…
Dual characterizations of norm minimization problems
Nguyen Duy Cuong
The paper studies a general norm minimization problem on a product of normed vector spaces. We establish dual necessary and sufficient optimality conditions and derive explicit for…
Metric constructions and fixed point theorems in product spaces
Doan Huu Hieu, Vo Minh Tam, Nguyen Duy Cuong
The paper studies a general scheme for constructing metrics on a product of metric spaces by means of a family of continuous convex functions. This construction includes the conven…
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…
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…
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…