5 papers · 1 filter
Properties of Generalized Polyhedral Convex Multifunctions
Nguyen Ngoc Luan, Nguyen Mau Nam, Nguyen Dong Yen
This paper presents a study of generalized polyhedral convexity under basic operations on multifunctions. We address the preservation of generalized polyhedral convexity under sums…
Relationships between Polyhedral Convex Sets and Generalized Polyhedral Convex Sets
Nguyen Ngoc Luan, Nguyen Mau Nam, Nguyen Nang Thieu +1
In this paper we study some relationships between polyhedral convex sets (PCS) and generalized polyhedral convex sets (GPCS). In particular, we clarify by a counterexample that the…
Two Optimal Value Functions in Parametric Conic Linear Programming
Nguyen Ngoc Luan, Do Sang Kim, Nguyen Dong Yen
We consider the conic linear program given by a closed convex cone in an Euclidean space and a matrix, where vector on the right-hand-side of the constraint system and the vector d…
A Representation of Generalized Convex Polyhedra and Applications
Nguyen Ngoc Luan, Nguyen Dong Yen
It is well known that finite-dimensional polyhedral convex sets can be generated by finitely many points and finitely many directions. Representation formulas in this spirit are ob…
Piecewise Linear Vector Optimization Problems on Locally Convex Hausdorff Topological Vector Spaces
Nguyen Ngoc Luan
Piecewise linear vector optimization problems in a locally convex Hausdorff topological vector spaces setting are considered in this paper. The efficient solution set of these prob…