Duong T. A. Nguyen

Duong T. A. Nguyen

Ph.D. Student

Talks and Posters

Distributed Nash Equilibrium Seeking over Time-Varying Directed Communication Networks

July 28, 2022

Talk, International Conference on Continuous Optimization (ICCOPT), Lehigh University, Bethlehem, PA

We propose a distributed gradient play algorithm for finding a Nash equilibrium (NE) in a class of non-cooperative convex games under partial information. In this algorithm, every agent performs agradient step to minimize its own cost function while sharing and retrieving information locally among its neighbors. The existing methods impose strong assumptions such as balancedness of the mixing matrices and global knowledge of the network communication structure, including Perron-Frobenius eigenvector of the adjacency matrix and other graph connectivity constants. In contrast, our approach relies only on a reasonable and widely-used assumption of row-stochasticity of the mixing matrices. We analyze the algorithm for time-varying directed graphs and prove its convergence to the NE, when the agents’ cost functions are strongly convex and have Lipschitz continuous gradients.

Market-based Mechanisms For Fair And Efficient Resource Allocation In Edge Computing

October 25, 2021

Talk, 2021 INFORMS Annual Meeting, Anaheim, CA

Edge computing enables novel Internet of Things applications and drastically enhances user experience. We propose a novel market equilibrium-based framework for allocating geographically distributed heterogeneous edge resources to competing services with diverse preferences in a fair and efficient manner. The proposed solution not only maximizes resource utilization but also gives each service its favorite resource bundle. Furthermore, the equilibrium allocation is Pareto-optimal and satisfies desired fairness properties including sharing incentive, proportionality, and envy-freeness. We also introduce privacy-preserving distributed algorithms for equilibrium computation.

Two-stage Robust Edge Service Placement And Sizing Under Uncertainties

October 24, 2021

Talk, 2021 INFORMS Annual Meeting, Anaheim, CA

We study the optimal service placement and workload allocation problem under uncertainties from the perspective of a service provider who can procure resources from numerous distributed edge nodes. To tackle this problem, we propose novel two-stage and multi-period robust optimization models which aim to balance between minimizing the operating cost for the provider and improving the experience for its users, considering various uncertainties such as resource demand and edge node failures. We employ and tailor the column-and-constraint generation method to develop iterative algorithms to solve the proposed robust models, which show significant advantages compared to benchmark solutions.

A comparative study of physics-informed deep learning models for discovering partial differential equations

February 28, 2020

Talk, LA/MS Sectional Meeting of the Mathematical Association of America, Loyola University, New Orleans, LA

In this work, we study physics-informed deep learning models to identify the general time-dependent nonlinear partial differential equations governing noisy data. We compare the performance of different regression techniques (LASSO, Ridge, TrainSTridge, and elastic net). We propose a different approach by employing pre-train neural networks to reduce the computation time.

A stable and accurate algorithm for a generalized Kirchhoff-Love plate model

October 17, 2019

Talk, Applied Mathematics Seminar, University of Louisiana at Lafayette, Lafayette, LA

In this paper, efficient and accurate numerical algorithms are developed to solve a generalized Kirchhoff–Love plate model subject to three common physical boundary conditions: (i) clamped; (ii) simply supported; and (iii) free. The generalization stems from the inclusion of additional physics to the classical Kirchhoff–Love model that accounts for bending only. We solve the model equation by discretizing the spatial derivatives using second-order finite-difference schemes, and then advancing the semi-discrete problem in time with either an explicit predictor–corrector or an implicit Newmark-Beta time-stepping algorithm.