5 citations · 13 across the 12 of their papers we have counts for
14 papers
Stability of Nonhomogeneous Split Equality and Split Feasibility Problems with Possibly Nonconvex Constraint Sets
Vu Thi Huong, Hong-Kun Xu, Nguyen Dong Yen
By applying some techniques of set-valued and variational analysis, we study solution stability of nonhomogeneous split equality problems and nonhomogeneous split feasibility probl…
Solving a Class of Nonconvex Quadratic Programs by Inertial DC Algorithms
Tran Hung Cuong, Yongdo Lim, Nguyen Nang Thieu +1
Two inertial DC algorithms for indefinite quadratic programs under linear constraints (IQPs) are considered in this paper. Using a qualification condition related to the normal con…
Fenchel Conjugate of Set-Valued Mappings
Nguyen Mau Nam, Gary Sandine, Nguyen Nang Thieu +1
In this paper, we present a novel concept of the Fenchel conjugate for set-valued mappings and investigate its properties in finite and infinite dimensions. After establishing the…
Nearly Convex Optimal Value Functions and Some Related Topics
Nguyen Quang Huy, Nguyen Mau Nam, Nguyen Dong Yen
In this paper, we introduce new properties of the relative interior calculus for nearly convex sets, functions, and set-valued mappings. These properties are important for the deve…
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…
Near Convexity and Generalized Differentiation
Nguyen Mau Nam, Nguyen Nang Thieu, Nguyen Dong Yen
In this paper, we introduce the concept of nearly convex set-valued mappings and investigate fundamental properties of these mappings. Additionally, we establish a geometric approa…
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…
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…
Subdifferential Stability Analysis for Convex Optimization Problems via Multiplier Sets
Duong Thi Viet An, Nguyen Dong Yen
This paper discusses differential stability of convex programming problems in Hausdorff locally convex topological vector spaces. Among other things, we obtain formulas for computi…
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…
A D.C. Algorithm via Convex Analysis Approach for Solving a Location Problem Involving Sets
Nguyen Thai An, Nguyen Mau Nam, Nguyen Dong Yen
We study a location problem that involves a weighted sum of distances to closed convex sets. As several of the weights might be negative, traditional solution methods of convex opt…