15 citations · 36 across the 26 of their papers we have counts for
29 papers · 1 filter
Lagrange Multipliers and Duality with Applications to Constrained Support Vector Machine
Nguyen Mau Nam, Gary Sandine, Quoc Tran-Dinh
In this paper, we employ the concept of quasi-relative interior to analyze the method of Lagrange multipliers and establish strong Lagrangian duality for nonsmooth convex optimizat…
Qualitative Analysis and Adaptive Boosted DCA for Generalized Multi-Source Weber Problems
Vo Si Trong Long, Nguyen Mau Nam, Tuyen Tran +1
This paper has two primary objectives. First, we investigate fundamental qualitative properties of the generalized multi-source Weber problem formulated using the Minkowski gauge f…
Generalized Relative Interiors and Generalized Convexity in Infinite Dimensions
Vo Si Trong Long, Boris Mordukhovich, Nguyen Mau Nam
This paper focuses on investigating generalized relative interior notions for sets in locally convex topological vector spaces with particular attentions to graphs of set-valued ma…
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…
Revisiting Rockafellar's Theorem on Relative Interiors of Convex Graphs with Applications to Convex Generalized Differentiation
Dang Van Cuong, Boris Mordukhovich, Nguyen Mau Nam +1
In this paper we revisit a theorem by Rockafellar on representing the relative interior of the graph of a convex set-valued mapping in terms of the relative interior of its domain…
Solving a Continuous Multifacility Location Problem by DC Algorithms
Anuj Bajaj, Boris Mordukhovich, Nguyen Mau Nam +1
The paper presents a new approach to solve multifacility location problems, which is based on mixed integer programming and algorithms for minimizing differences of convex (DC) fun…
Quasi-Relative Interiors for Graphs of Convex Set-Valued Mappings
Dang Van Cuong, Boris S. Mordukhovich, Nguyen Mau Nam
This paper aims at providing further studies of the notion of quasi-relative interior for convex sets introduced by Borwein and Lewis. We obtain new formulas for representing quasi…
Subgradients of Minimal Time Functions without Calmness
Nguyen Mau Nam, Dang Van Cuong
In recent years there has been great interest in variational analysis of a class of nonsmooth functions called the minimal time function. In this paper we continue this line of res…
Nesterov's Smoothing Technique and Minimizing Differences of Convex Functions for Hierarchical Clustering
Nguyen Mau Nam, Wondi Geremew, Sam Raynolds +1
A bilevel hierarchical clustering model is commonly used in designing optimal multicast networks. In this paper, we consider two different formulations of the bilevel hierarchical…
Extremality of Convex Sets with Some Applications
Boris Mordukhovich, Nguyen Mau Nam
In this paper we introduce an enhanced notion of extremal systems for sets in locally convex topological vector spaces and obtain efficient conditions for set extremality in the co…
Variational Geometric Approach to Generalized Differential and Fenchel Conjugate Calculi in Convex Analysis
Boris Mordukhovich, Nguyen Mau Nam, R. Blake Rector +1
This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. B…
Minimizing Differences of Convex Functions and Applications to Facility Location and Clustering
Nguyen Mau Nam, R. Blake Rector, Daniel Giles
In this paper we develop algorithms to solve generalized weighted Fermat-Torricelli problems with positive and negative weights and multifacility location problems involving distan…
Geometric Approach to Subdifferential Calculus
Boris Mordukhovich, Nguyen Mau Nam
In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows…
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…
Generalized Differentiation and Characterizations for Differentiability of Infimal Convolutions
Nguyen Mau Nam, Dang Van Cuong
This paper is devoted to the study of generalized differentiation properties of the infimal convolution. This class of functions covers a large spectrum of nonsmooth functions well…
Subdifferential Formulas for a Class of Nonconvex Infimal Convolutions
Nguyen Mau Nam
In this paper, we provide a number of subdifferential formulas for a class of nonconvex infimal convolutions in normed spaces. The formulas obtained unify several results on subdif…
A Unified Approach to Convex and Convexified Generalized Differentiation of Nonsmooth Functions and Set-Valued Mappings
Nguyen Mau Nam, Nguyen Dinh Hoang, R. Blake Rector
In the early 1960's, Moreau and Rockafellar introduced a concept of called \emph{subgradient} for convex functions, initiating the developments of theoretical and applied convex an…
The Log-Exponential Smoothing Technique and Nesterov's Accelerated Gradient Method for Generalized Sylvester Problems
Nguyen Thai An, Daniel Giles, Nguyen Mau Nam +1
The Sylvester smallest enclosing circle problem involves finding the smallest circle that encloses a finite number of points in the plane. We consider generalized versions of the S…
Subgradient Algorithm, Stochastic Subgradient Algorithm, Incremental Subgradient Algorithm, and Set Location Problems
Nguyen Mau Nam, Nguyen Thai An, Han Le
In recent years, important progress has been made in applying methods and techniques of convex optimization to many fields of applications such as location science, engineering, co…
The Fermat-Torricelli Problem and Weiszfeld's Algorithm in the Light of Convex Analysis
Boris Mordukhovich, Nguyen Mau Nam
In the early 17th century, Pierre de Fermat proposed the following problem: given three points in the plane, find a point such that the sum of its Euclidean distances to the three…