5 papers
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…
Optimality conditions based on the Fréchet second-order subdifferential
Duong Thi Viet An, Nguyen Dong Yen
This paper focuses on second-order necessary optimality conditions for constrained optimization problems on Banach spaces. For problems in the classical setting, where the objectiv…
Sensitivity Analysis of a Stationary Point Set Map under Total Perturbations. Part 1: Lipschitzian Stability
Duong Thi Kim Huyen, Jen-Chih Yao, Nguyen Dong Yen
By applying some theorems of Levy and Mordukhovich (Math Program 99: 311--327, 2004) and other related results, we estimate the Fréchet coderivative and the Mordukhovich coderivati…
Sensitivity Analysis of a Stationary Point Set Map under Total Perturbations. Part 2: Robinson Stability
Duong Thi Kim Huyen, Jen-Chih Yao, Nguyen Dong Yen
In Part 1 of this paper, we have estimated the Fréchet coderivative and the Mordukhovich coderivative of the stationary point set map of a smooth parametric optimization problem wi…
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…