5 papers · 1 filter
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…
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…
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…