N. Dinh
YOU?
Author Swipe
View article: Primal and Dual Characterizations for Farkas Type Lemmas in Terms of Closedness Criteria
Primal and Dual Characterizations for Farkas Type Lemmas in Terms of Closedness Criteria Open
This paper deals with the characterization, in terms of closedness of certain sets regarding other sets, of Farkas lemmas determining when the upperlevel set of a convex function $f$ contains a set of the form $C\cap \mathbb{A}^{-1}\left…
View article: Fatal Mycobacterium avium meningitis in an HIV-negative Vietnamese man: a case report
Fatal Mycobacterium avium meningitis in an HIV-negative Vietnamese man: a case report Open
Background Nontuberculous mycobacteria are environmental mycobacteria that rarely cause human disease, especially in the central nervous system. Central nervous system infection by Mycobacterium avium complex, the most common pathogen amon…
View article: Stable strong duality for cone-constrained set-valued optimization problems: A perturbation approach
Stable strong duality for cone-constrained set-valued optimization problems: A perturbation approach Open
In this paper we consider a general set-valued otimimization problem of the model Winf F(x), s.t. x in X where $F\colon X\rightrightarrows Y\cup\{+\infty_{Y}\}$ is a proper mapping. The problem is then embed into a parametric problem and c…
View article: Relaxed Lagrangian duality in convex infinite optimization: Reverse strong duality and optimality
Relaxed Lagrangian duality in convex infinite optimization: Reverse strong duality and optimality Open
We associate with each convex optimization problem posed on some locally convex space with an infinite index set T, and a given non-empty family H formed by finite subsets of T, a suitable Lagrangian-Haar dual problem.We provide reverse H …
View article: Relaxed Lagrangian duality in convex infinite optimization: reverse strong duality and optimality
Relaxed Lagrangian duality in convex infinite optimization: reverse strong duality and optimality Open
We associate with each convex optimization problem posed on some locally convex space with an infinite index set T, and a given non-empty family H formed by finite subsets of T, a suitable Lagrangian-Haar dual problem. We provide reverse H…
View article: Simple Bilevel Programming and Extensions, Part-1: Theory
Simple Bilevel Programming and Extensions, Part-1: Theory Open
In this paper we begin by discussing the simple bilevel programming problem (SBP) and its extension the simple mathematical programming problem under equilibrium constraints (SMPEC). Here we first define both these problems and study their…
View article: Simple Bilevel Programming and Extensions Part-II: Algorithms
Simple Bilevel Programming and Extensions Part-II: Algorithms Open
This article continues our study on simple bilevel and simple MPEC problems. In this article we focus on developing algorithms. We show how using the idea of a gap function one can represent a simple MPEC as a simple bilevel problem with n…
View article: Sectional convexity of epigraphs of conjugate mappings with applications to robust vector duality
Sectional convexity of epigraphs of conjugate mappings with applications to robust vector duality Open
This paper concerns the robust vector problems \begin{equation*} \mathrm{(RVP)}\ \ {\rm Wmin}\left\{ F(x): x\in C,\; G_u(x)\in -S,\;\forall u\in\mathcal{U}\right\}, \end{equation*} where $X, Y, Z$ are locally convex Hausdorff topological v…
View article: Duality for Robust Linear Infinite Programming Problems Revisited
Duality for Robust Linear Infinite Programming Problems Revisited Open
In this paper, we consider the robust linear infinite programming problem $({\rm RLIP}_c) $ defined by \begin{eqnarray*} ({\rm RLIP}_c)\quad &&\inf\; \langle c,x\rangle \textrm{subject to } &&x\in X,\; \langle x^\ast,x \rangle \le r ,\;\fo…
View article: Asymptotic Farkas lemmas for convex systems
Asymptotic Farkas lemmas for convex systems Open
In this paper we establish characterizations of the containment of the set {xX: xC,g(x)K}{xX: f (x)0}, where C is a closed convex subset of a locally convex Hausdorff topological vector space, X, K is a closed convex cone in another…
View article: An approximate Hahn-Banach-Lagrange theorem
An approximate Hahn-Banach-Lagrange theorem Open
In this paper, we proved a new extended version of the Hahn-Banach-Lagrange theorem that is valid in the absence of a qualification condition and is called an approximate Hahn-Banach-Lagrange theorem. This result, in special cases, gives r…
View article: Robust optimization revisited via robust vector Farkas lemmas
Robust optimization revisited via robust vector Farkas lemmas Open
This paper provides characterizations of the weakly minimal elements of vector optimization problems and the global minima of scalar optimization problems posed on locally convex spaces whose objective functions are deterministic while the…
View article: Characterizing weak solutions for vector optimization problems
Characterizing weak solutions for vector optimization problems Open
This paper provides characterizations of the weak solutions of optimization problems where a given vector function $F,$ from a decision space $X$ to an objective space $Y$, is "minimized" on the set of elements $x\in C$ (where $C\subset X$…