Trung Nghia Nguyen

Trung Nghia Nguyen

PhD student at Department of Statistics and Operations Research, University of North Carolina at Chapel Hill

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Pages

Posts

Future Blog Post

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This post will show up by default. To disable scheduling of future posts, edit config.yml and set future: false.

Blog Post number 4

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This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

Blog Post number 3

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Blog Post number 2

less than 1 minute read

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Blog Post number 1

less than 1 minute read

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This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.

portfolio

publications

talks

A strong convergence theorem for an iterative method for solving the multiple-sets split feasibility problem in Hilbert spaces

Published:

Abstract: There are many iterative methods for solving the multiple-sets split feasibility problem involving step sizes that depend on the norm of a bounded linear operator F. The implementation of such algorithms is usually difficult to handle with because one haas to compute the norm of the operator F. In this talk, we introduce a new iterative algorithm for approximating a solution of a class of multiple-sets split feasibility problem without prior knowledge of operator norms. Strong convergence of the iterative process is proved. Then, we recapitulate the two methods for this class of problem which were given by Nguyen Buong (Iterative algorithms for the multiple-sets split feasibility problem in Hilbert spaces, Numer. Algor. 76 (2017), 783–798) and by Tran Viet Anh (A parallel method for variational inequalities with the multiple-sets split feasibility problem constraints, J. Fixed Point Theory Appl. 19 (2017), 2681–2696). A numerical example is given to illustrate the proposed iterative algorithm and compare it with the methods of Buong and Anh.

Semidefinite programming and an application in combinatorics

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Abstract: As a subfield of convex optimization, semidefinite programming (SDP) was the most exciting development in mathematical programming in the 1990’s, thanks to its several applications in control theory, robust optimization, combinatorial optimization and eigenvalue optimization. Along with linear programming and quadratic programming, SDP has become one of the basic modeling and optimization tools, as more and more problems are modeled as semidefinite programs. In this talk, we introduce some fundamental concepts of SDP and related issues. To be more specific, we talk about semidefinite cone, semidefinite programming and semidefinite representability of a convex set in the relationship with conic quadratic representability. One application of SDP in the problem of stability number of a graph with Lovasz’s approach is considered in the last section.

A new self-adaptive algorithm for solving the multiple-set split variational inequality problem in Hilbert spaces

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Abstract: In this talk, we introduce a new self-adaptive algorithm for solving the multiple-set split variational inequality problem in Hilbert spaces. Our algorithm uses dynamic step-sizes, chosen based on information of the previous step. In comparison with the work by Censor et al. (Numer. Algor., 59:301–323, 2012), the new algorithm gives strong convergence results and does not require information about the transformation operator’s norm. Some applications of our main results regarding the solution of multiple-set split feasibility problem and the split feasibility problem are presented and show that the iterative method converges strongly under weaker assumptions than the ones used recently by Xu (Inverse Problems, 22:2021–2034, 2006) and by Buong (Numer. Algor., 76:783–798, 2017). Numerical experiments on finite-dimensional and infinite-dimensional spaces and an application to discrete optimal control problems are reported to demonstrate the advantages and efficiency of the proposed algorithms over some existing results.

A new hybrid projection - proximal point algorithm for solving the multiple-set split variational inequality problem in Hilbert spaces

Published:

Abstract: In this talk, we study the multiple-set split variational inequality problem in Hilbert spaces. Before presenting the new algorithm, we talk about a way for the implementation of hybrid projection method, in which we compute the projection of a given point onto the intersection of a finite system of closed convex sets in some special cases. Then, we propose a new algorithm combining the hybrid projection method with the proximal point algorithm, and establish a strong convergence theorem for it. Some applications of our main results regarding the solution of the split variational inequality problem and the multiple-set split feasibility problem are presented and show that the iterative method converges strongly under weaker assumptions than the ones used recently by Anh (J. Fixed Point Theory Appl. 19:2681–2696, 2017), Buong (Numer. Algorithms, 76:783–798, 2017) and Xu (Inverse Problems, 22:2021– 2034, 2006). Some numerical examples are also given to illustrate the convergence analysis of the considered method.

New hybrid projection method and shrinking projection method for solving the multiple-set split variational inequality problem in Hilbert spaces

Published:

Abstract: In this talk, we study the multiple-set split variational inequality problem with monotone and Lipschitz continuous operators in real Hilbert spaces. Our new algorithms for solving this problem are based on the calculation of the metric projection onto the intersection of finite convex sets. To be more specific, we propose two new algorithms combining the proximal point algorithm with the hybrid projection method or the shrinking projection method. The strong convergence theorems for them are established under some feasible assumptions. Next, in some deduced cases, we obtained some results which are equivalent to the algorithms introduced by K. Nakajo and W. Takahashi (J. Math. Anal. Appl., 279, 372–379, 2003) and W. Takahashi (J. Math. Anal. Appl., 341(1), 276–286, 2008). Some numerical examples are also given to illustrate the convergence analysis of the proposed methods.

teaching

Fall 2022 - STOR 215: Foundation of Decision Science

Undergraduate course, Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, 2022

Introduction to basic concepts and techniques of discrete mathematics with applications to business and social and physical sciences. Topics include logic, sets, functions, combinatorics, discrete probability, graphs, and networks.

Spring 2023 - STOR 113: Decision Models for Business and Economics

Undergraduate course, Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, 2023

This course equips you with essential skills for solving quantitative problems in business and economics. We’ll begin by investigating some basic models which appear repeatedly in applied settings – linear models, quadratic models, and exponential models. Marginal analysis – the analysis of the rate of change of one quantity with respect to another – will be covered next. The course culminates in a module on optimization, the set of techniques for finding the minimum or the maximum of a variable quantity such as cost, revenue, or profit. Applications covered along the way include compound interest, market equilibrium, and price and income elasticity. Much of our time in and out of lecture will be devoted to reviewing relevant algebra concepts, and learning differential calculus – the mathematical language for analyzing rates of change.

Summer 2023 (Session 1) - STOR 155: Introduction to Data Models and Inference

Undergraduate course, Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, 2023

Data analysis; correlation and regression; sampling and experimental design; basic probability (random variables, expected values, normal and binomial distributions); hypothesis testing and confidence intervals for means, proportions, and regression parameters; use of spreadsheet software.

Summer 2023 (Session 2) - STOR 155: Introduction to Data Models and Inference

Undergraduate course, Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, 2023

Data analysis; correlation and regression; sampling and experimental design; basic probability (random variables, expected values, normal and binomial distributions); hypothesis testing and confidence intervals for means, proportions, and regression parameters; use of spreadsheet software.