arXiv subjects

Duong Thuy Anh Nguyen

Publications and source records attributed to Duong Thuy Anh Nguyen.

17 recordsLinked to original sources

arXiv2026

Efficient Graph Partitioning under Resource Constraints: A Cutting-Plane Framework for Distribution Grids

This paper presents an optimal network topology control framework using cutting-plane methods for efficient network partitioning with controllable edges. The objective is to enable real-time reconfiguration of interconnected subnetworks while ensuring radial connectivity, resource feasibility, and structured leader allocation, which provide structural foundations for distributed controllability, stability, and coordination. The problem is formulated as a mixed-integer program that integrates graph-theoretic constraints, resource flow, and network structural properties to enforce an operational hierarchy. To address the combinatorial complexity of cycle elimination and leader assignment, we propose an iterative cutting-plane framework that ensures convergence to an optimal and feasible network topology. Theoretical guarantees on optimality preservation, feasibility, and convergence are established, ensuring systematic elimination of infeasible configurations while preserving the required coordination structure. Simulations on a modified Iowa 240-bus power distribution grid demonstrate the framework's effectiveness in network reconfiguration under resource constraints. The approach achieves a median speedup of 65.4x and a best-case speedup of over 78x in a 46-switch configuration.

math.OC↗

arXiv2025

A Mixed-Integer Bi-level Model for Joint Optimal Edge Resource Pricing and Provisioning

This paper studies the joint optimization of edge node activation and resource pricing in edge computing, where an edge computing platform provides heterogeneous resources to accommodate multiple services with diverse preferences. We cast this problem as a bi-level program, with the platform acting as the leader and the services as the followers. The platform aims to maximize net profit by optimizing edge resource prices and edge node activation, with the services' optimization problems acting as constraints. Based on the platform's decisions, each service aims to minimize its costs and enhance user experience through optimal service placement and resource procurement decisions. The presence of integer variables in both the upper and lower-level problems renders this problem particularly challenging. Traditional techniques for transforming bi-level problems into single-level formulations are inappropriate owing to the non-convex nature of the follower problems. Drawing inspiration from the column-and-constraint generation method in robust optimization, we develop an efficient decomposition-based iterative algorithm to compute an exact optimal solution to the formulated bi-level problem. Extensive numerical results are presented to demonstrate the efficacy of the proposed model and technique.

math.OC↗

arXiv2025

Delay-Aware Robust Edge Network Hardening Under Decision-Dependent Uncertainty

Edge computing promises to offer low-latency and ubiquitous computation to numerous devices at the network edge. For delay-sensitive applications, link delays can have a direct impact on service quality. These delays can fluctuate drastically over time due to various factors such as network congestion, changing traffic conditions, cyberattacks, component failures, and natural disasters. Thus, it is crucial to efficiently harden the edge network to mitigate link delay variation as well as ensure a stable and improved user experience. To this end, we propose a novel robust model for optimal edge network hardening, considering the link delay uncertainty. Departing from the existing literature that treats uncertainties as exogenous, our model incorporates an endogenous uncertainty set to properly capture the impact of hardening and workload allocation decisions on link delays. However, the endogenous set introduces additional complexity to the problem due to the interdependence between decisions and uncertainties. We present two efficient methods to transform the problem into a solvable form. Extensive numerical results are shown to demonstrate the effectiveness of the proposed approach.

cs.NI↗

arXiv2024

Robust Dynamic Edge Service Placement Under Spatio-Temporal Correlated Demand Uncertainty

Edge computing allows Service Providers (SPs) to enhance user experience by placing their services closer to the network edge. Determining the optimal provisioning of edge resources to meet the varying and uncertain demand cost-effectively is a critical task for SPs. This paper introduces a novel two-stage multi-period robust model for edge service placement and workload allocation, aiming to minimize the SP's operating costs while ensuring service quality. The salient feature of this model lies in its ability to enable SPs to utilize dynamic service placement and leverage spatio-temporal correlation in demand uncertainties to mitigate the inherent conservatism of robust solutions. In our model, resource reservation is optimized in the initial stage, preemptively, before the actual demand is disclosed, whereas dynamic service placement and workload allocation are determined in the subsequent stage, following the revelation of uncertainties. To address the challenges posed by integer recourse variables in the second stage of the resulting tri-level adjustable robust optimization problem, we propose a novel iterative, decomposition-based approach, ensuring finite convergence to an exact optimal solution. Extensive numerical results are provided to demonstrate the efficacy of the proposed model and approach.

math.OC↗

arXiv2024

Distributed Nash Equilibrium Seeking over Time-Varying Directed Communication Networks

This paper proposes a distributed algorithm to find the Nash equilibrium in a class of non-cooperative convex games with partial-decision information. Our method employs a distributed projected gradient play approach alongside consensus dynamics, with individual agents minimizing their local costs through gradient steps and local information exchange with neighbors via a time-varying directed communication network. Addressing time-varying directed graphs presents significant challenges. Existing methods often circumvent this by focusing on static graphs or specific types of directed graphs or by requiring the stepsizes to scale with the Perron-Frobenius eigenvectors. In contrast, we establish novel results that provide a contraction property for the mixing terms associated with time-varying row-stochastic weight matrices. Our approach explicitly expresses the contraction coefficient based on the characteristics of the weight matrices and graph connectivity structures, rather than implicitly through the second-largest singular value of the weight matrix as in prior studies. The established results facilitate proving geometric convergence of the proposed algorithm and advance convergence analysis for distributed algorithms in time-varying directed communication networks. Numerical results on a Nash-Cournot game demonstrate the efficacy of the proposed method.

cs.GT↗

arXiv2024

Decentralized Federated Learning with Gradient Tracking over Time-Varying Directed Networks

We investigate the problem of agent-to-agent interaction in decentralized (federated) learning over time-varying directed graphs, and, in doing so, propose a consensus-based algorithm called DSGTm-TV. The proposed algorithm incorporates gradient tracking and heavy-ball momentum to distributively optimize a global objective function, while preserving local data privacy. Under DSGTm-TV, agents will update local model parameters and gradient estimates using information exchange with neighboring agents enabled through row- and column-stochastic mixing matrices, which we show guarantee both consensus and optimality. Our analysis establishes that DSGTm-TV exhibits linear convergence to the exact global optimum when exact gradient information is available, and converges in expectation to a neighborhood of the global optimum when employing stochastic gradients. Moreover, in contrast to existing methods, DSGTm-TV preserves convergence for networks with uncoordinated stepsizes and momentum parameters, for which we provide explicit bounds. These results enable agents to operate in a fully decentralized manner, independently optimizing their local hyper-parameters. We demonstrate the efficacy of our approach via comparisons with state-of-the-art baselines on real-world image classification and natural language processing tasks.

math.OC↗

arXiv2024

Constrained multi-cluster game: Distributed Nash equilibrium seeking over directed graphs

Motivated by the complex dynamics of cooperative and competitive interactions within networked agent systems, multi-cluster games provide a framework for modeling the interconnected goals of self-interested clusters of agents. For this setup, the existing literature lacks comprehensive gradient-based solutions that simultaneously consider constraint sets and directed communication networks, both of which are crucial for many practical applications. To address this gap, this paper proposes a distributed Nash equilibrium seeking algorithm that integrates consensus-based methods and gradient-tracking techniques, where inter-cluster and intra-cluster communications only use row- and column-stochastic weight matrices, respectively. To handle constraints, we introduce an averaging procedure, which can effectively address the complications associated with projections. In turn, we can show linear convergence of our algorithm, focusing on the contraction property of the optimality gap. We demonstrate the efficacy of the proposed algorithm through a microgrid energy management application.

math.OC↗

arXiv2024

Two-Stage Distributionally Robust Edge Node Placement Under Endogenous Demand Uncertainty

Edge computing (EC) promises to deliver low-latency and ubiquitous computation to numerous devices at the network edge. This paper aims to jointly optimize edge node (EN) placement and resource allocation for an EC platform, considering demand uncertainty. Diverging from existing approaches treating uncertainties as exogenous, we propose a novel two-stage decision-dependent distributionally robust optimization (DRO) framework to effectively capture the interdependence between EN placement decisions and uncertain demands. The first stage involves making EN placement decisions, while the second stage optimizes resource allocation after uncertainty revelation. We present an exact mixed-integer linear program reformulation for solving the underlying ``min-max-min" two-stage model. We further introduce a valid inequality method to enhance computational efficiency, especially for large-scale networks. Extensive numerical experiments demonstrate the benefits of considering endogenous uncertainties and the advantages of the proposed model and approach.

math.OC↗

arXiv2023

Distributed Stochastic Optimization with Gradient Tracking over Time-Varying Directed Networks

We study a distributed method called SAB-TV, which employs gradient tracking to collaboratively minimize the sum of smooth and strongly-convex local cost functions for networked agents communicating over a time-varying directed graph. Each agent, assumed to have access to a stochastic first-order oracle for obtaining an unbiased estimate of the gradient of its local cost function, maintains an auxiliary variable to asymptotically track the stochastic gradient of the global cost. The optimal decision and gradient tracking are updated over time through limited information exchange with local neighbors using row- and column-stochastic weights, guaranteeing both consensus and optimality. With a sufficiently small constant step-size, we demonstrate that, in expectation, SAB-TV converges linearly to a neighborhood of the optimal solution. Numerical simulations illustrate the effectiveness of the proposed algorithm.

math.OC↗

arXiv2023

Optimal Workload Allocation for Distributed Edge Clouds With Renewable Energy and Battery Storage

This paper studies an optimal workload allocation problem for a network of renewable energy-powered edge clouds that serve users located across various geographical areas. Specifically, each edge cloud is furnished with both an on-site renewable energy generation unit and a battery storage unit. Due to the discrepancy in electricity pricing and the diverse temporal-spatial characteristics of renewable energy generation, how to optimally allocate workload to different edge clouds to minimize the total operating cost while maximizing renewable energy utilization is a crucial and challenging problem. To this end, we introduce and formulate an optimization-based framework designed for Edge Service Providers (ESPs) with the overarching goal of simultaneously reducing energy costs and environmental impacts through the integration of renewable energy sources and battery storage systems, all while maintaining essential quality-of-service standards. Numerical results demonstrate the effectiveness of the proposed model and solution in maintaining service quality as well as reducing operational costs and emissions. Furthermore, the impacts of renewable energy generation and battery storage on optimal system operations are rigorously analyzed.

math.OC↗

arXiv2023

Nash equilibrium seeking over digraphs with row-stochastic matrices and network-independent step-sizes

In this paper, we address the challenge of Nash equilibrium (NE) seeking in non-cooperative convex games with partial-decision information. We propose a distributed algorithm, where each agent refines its strategy through projected-gradient steps and an averaging procedure. Each agent uses estimates of competitors' actions obtained solely from local neighbor interactions, in a directed communication network. Unlike previous approaches that rely on (strong) monotonicity assumptions, this work establishes the convergence towards a NE under a diagonal dominance property of the pseudo-gradient mapping, that can be checked locally by the agents. Further, this condition is physically interpretable and of relevance for many applications, as it suggests that an agent's objective function is primarily influenced by its individual strategic decisions, rather than by the actions of its competitors. In virtue of a novel block-infinity norm convergence argument, we provide explicit bounds for constant step-size that are independent of the communication structure, and can be computed in a totally decentralized way. Numerical simulations on an optical network's power control problem validate the algorithm's effectiveness.

cs.GT↗

arXiv2023

Accelerated $AB$/Push-Pull Methods for Distributed Optimization over Time-Varying Directed Networks

This paper investigates a novel approach for solving the distributed optimization problem in which multiple agents collaborate to find the global decision that minimizes the sum of their individual cost functions. First, the $AB$/Push-Pull gradient-based algorithm is considered, which employs row- and column-stochastic weights simultaneously to track the optimal decision and the gradient of the global cost function, ensuring consensus on the optimal decision. Building on this algorithm, we then develop a general algorithm that incorporates acceleration techniques, such as heavy-ball momentum and Nesterov momentum, as well as their combination with non-identical momentum parameters. Previous literature has established the effectiveness of acceleration methods for various gradient-based distributed algorithms and demonstrated linear convergence for static directed communication networks. In contrast, we focus on time-varying directed communication networks and establish linear convergence of the methods to the optimal solution, when the agents' cost functions are smooth and strongly convex. Additionally, we provide explicit bounds for the step-size value and momentum parameters, based on the properties of the cost functions, the mixing matrices, and the graph connectivity structures. Our numerical results illustrate the benefits of the proposed acceleration techniques on the $AB$/Push-Pull algorithm.

math.OC↗

arXiv2023

Geometric Convergence of Distributed Heavy-Ball Nash Equilibrium Algorithm over Time-Varying Digraphs with Unconstrained Actions

This paper presents a new distributed algorithm that leverages heavy-ball momentum and a consensus-based gradient method to find a Nash equilibrium (NE) in a class of non-cooperative convex games with unconstrained action sets. In this approach, each agent in the game has access to its own smooth local cost function and can exchange information with its neighbors over a communication network. The main novelty of our work is the incorporation of heavy-ball momentum in the context of non-cooperative games that operate on fully-decentralized, directed, and time-varying communication graphs, while also accommodating non-identical step-sizes and momentum parameters. Overcoming technical challenges arising from the dynamic and asymmetric nature of mixing matrices and the presence of an additional momentum term, we provide a rigorous proof of the geometric convergence to the NE. Moreover, we establish explicit bounds for the step-size values and momentum parameters based on the characteristics of the cost functions, mixing matrices, and graph connectivity structures. We perform numerical simulations on a Nash-Cournot game to demonstrate accelerated convergence of the proposed algorithm compared to that of the existing methods.

cs.GT↗

arXiv2023

CrowdCache: A Decentralized Game-Theoretic Framework for Mobile Edge Content Sharing

Mobile edge computing (MEC) is a promising solution for enhancing the user experience, minimizing content delivery expenses, and reducing backhaul traffic. In this paper, we propose a novel privacy-preserving decentralized game-theoretic framework for resource crowdsourcing in MEC. Our framework models the interactions between a content provider (CP) and multiple mobile edge device users (MEDs) as a non-cooperative game, in which MEDs offer idle storage resources for content caching in exchange for rewards. We introduce efficient decentralized gradient play algorithms for Nash equilibrium (NE) computation by exchanging local information among neighboring MEDs only, thus preventing attackers from learning users' private information. The key challenge in designing such algorithms is that communication among MEDs is not fixed and is facilitated by a sequence of undirected time-varying graphs. Our approach achieves linear convergence to the NE without imposing any assumptions on the values of parameters in the local objective functions, such as requiring strong monotonicity to be stronger than its dependence on other MEDs' actions, which is commonly required in existing literature when the graph is directed time-varying. Extensive simulations demonstrate the effectiveness of our approach in achieving efficient resource outsourcing decisions while preserving the privacy of the edge devices.

cs.GT↗

arXiv2023

A Bandit Approach to Online Pricing for Heterogeneous Edge Resource Allocation

Edge Computing (EC) offers a superior user experience by positioning cloud resources in close proximity to end users. The challenge of allocating edge resources efficiently while maximizing profit for the EC platform remains a sophisticated problem, especially with the added complexity of the online arrival of resource requests. To address this challenge, we propose to cast the problem as a multi-armed bandit problem and develop two novel online pricing mechanisms, the Kullback-Leibler Upper Confidence Bound (KL-UCB) algorithm and the Min-Max Optimal algorithm, for heterogeneous edge resource allocation. These mechanisms operate in real-time and do not require prior knowledge of demand distribution, which can be difficult to obtain in practice. The proposed posted pricing schemes allow users to select and pay for their preferred resources, with the platform dynamically adjusting resource prices based on observed historical data. Numerical results show the advantages of the proposed mechanisms compared to several benchmark schemes derived from traditional bandit algorithms, including the Epsilon-Greedy, basic UCB, and Thompson Sampling algorithms.

cs.LG↗

arXiv2023

A Fairness-Aware Attacker-Defender Model for Optimal Edge Network Operation and Protection

While various aspects of edge computing (EC) have been studied extensively, the current literature has overlooked the robust edge network operations and planning problem. To this end, this letter proposes a novel fairness-aware attacker-defender model for optimal edge network operation and hardening against possible attacks and disruptions. The proposed model helps EC platforms identify the set of most critical nodes to be protected to mitigate the impact of failures on system performance. Numerical results show that the proposed solution can not only ensure good service quality but also maintain fairness among different areas during disruptions.

math.OC↗

arXiv2022

AB/Push-Pull Method for Distributed Optimization in Time-Varying Directed Networks

In this paper, we study the distributed optimization problem for a system of agents embedded in time-varying directed communication networks. Each agent has its own cost function and agents cooperate to determine the global decision that minimizes the summation of all individual cost functions. We consider the so-called push-pull gradient-based algorithm (termed as AB/Push-Pull) which employs both row- and column-stochastic weights simultaneously to track the optimal decision and the gradient of the global cost while ensuring consensus and optimality. We show that the algorithm converges linearly to the optimal solution over a time-varying directed network for a constant stepsize when the agent's cost function is smooth and strongly convex. The linear convergence of the method has been shown in Saadatniaki et al. (2020), where the multi-step consensus contraction parameters for row- and column-stochastic mixing matrices are not directly related to the underlying graph structure, and the explicit range for the stepsize value is not provided. With respect to Saadatniaki et al. (2020), the novelty of this work is twofold: (1) we establish the one-step consensus contraction for both row- and column-stochastic mixing matrices with the contraction parameters given explicitly in terms of the graph diameter and other graph properties; and (2) we provide explicit upper bounds for the stepsize value in terms of the properties of the cost functions, the mixing matrices, and the graph connectivity structure.

math.OC↗