Minh N. Dao

Minh N. Dao
RMIT University | RMIT · Department of Mathematical Sciences

PhD

About

87
Publications
13,639
Reads
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1,319
Citations
Additional affiliations
July 2020 - October 2022
Federation University
Position
  • Lecturer
October 2019 - June 2020
UNSW Sydney
Position
  • Research Associate
September 2013 - August 2014
National Institute for Applied Sciences Tolouse
Position
  • Teaching and Research Temporary Attaché
Education
October 2010 - September 2014
Université Toulouse III - Paul Sabatier
Field of study
  • Applied Mathematics

Publications

Publications (87)
Preprint
Full-text available
In this paper, under the monotonicity of pairs of operators, we propose some Generalized Proximal Point Algorithms to solve non-monotone inclusions using warped resolvents and transformed resolvents. The weak, strong, and linear convergence of the proposed algorithms are established under very mild conditions.
Preprint
Full-text available
We consider trust-region methods for solving optimization problems where the objective is the sum of a smooth, nonconvex function and a nonsmooth, convex regularizer. We extend the global convergence theory of such methods to include worst-case complexity bounds in the case of unbounded model Hessian growth, and introduce a new, simple nonsmooth tr...
Preprint
Full-text available
In this paper, we propose a distributed first-order algorithm with backtracking linesearch for solving multi-agent minimisation problems, where each agent handles a local objective involving nonsmooth and smooth components. Unlike existing methods that require global Lipschitz continuity and predefined stepsizes, our algorithm adjusts stepsizes usi...
Article
Full-text available
In this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth functions and a smooth function, coupled by a difference of functions. This structure encapsulates numerous sign...
Preprint
Full-text available
The difference-of-convex (DC) program is a crucial approach to nonconvex optimization problems due to its structure, which encompasses a wide ranges of practical applications. In this paper, we aim to tackle a generalized class of DC programs, where the objective function is formed by summing a possibly nonsmooth nonconvex function and a differenti...
Article
Full-text available
The penetration of distributed energy resources (DERs) such as photovoltaic systems, energy storage systems, and electric vehicles is increasing in the distribution system. The distinct characteristics of these resources, e.g., volatility and intermittency, introduce complexity in operation and planning of the distribution system. This paper first...
Preprint
Full-text available
The penetration of distributed energy resources (DERs) such as photovoltaic systems, energy storage systems, and electric vehicles is increasing in the distribution system. The distinct characteristics of these resources, e.g., volatility and intermittency, introduce complexity in operation and planning of the distribution system. This paper first...
Article
Full-text available
This work proposes novel approaches that jointly design user equipment (UE) association and power control (PC) in a downlink user-centric cell-free massive multiple-input multiple-output (CFmMIMO) network, where each UE is only served by a set of access points (APs) for reducing the fronthaul signalling and computational complexity. In order to max...
Preprint
Full-text available
In this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth functions and a smooth function, coupled by a difference of functions. This structure encapsulates numerous sign...
Preprint
Full-text available
We prove that the Douglas-Rachford method applied to two closed convex cones in the Euclidean plane converges in finitely many steps if and only if the set of fixed points of the Douglas-Rachford operator is nontrivial. We analyze this special case using circle dynamics. We also construct explicit examples for a broad family of projection methods f...
Article
In this paper, we are interested in studying the asymptotic behavior of the solutions of differential inclusions governed by maximally monotone operators. In the case where the LaSalle’s invariance principle is inconclusive, we provide a refined version of the invariance principle theorem. This result derives from the problem of locating the -limit...
Article
Full-text available
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous gradient, subtracted by a weakly convex function. This general framework allows us to tackle problems invo...
Conference Paper
Full-text available
This work proposes a novel approach that jointly designs user equipment (UE) association and power control in a downlink user-centric cell-free massive multiple-input multiple-output (CFmMIMO) network, where each access point (AP) only serves only a set of its associated UEs for reducing the backhaul signaling and computational complexity. Aiming a...
Article
Full-text available
Non-independent and identically distributed (non-IID) data distribution among clients is considered as the key factor that degrades the performance of federated learning (FL). Several approaches to handle non-IID data, such as personalized FL and federated multitask learning (FMTL), are of great interest to research communities. In this work, first...
Article
Full-text available
This work proposes novel synchronous, asyn-chronous, and session-based designs for energy-efficient massive multiple-input multiple-output networks to support federated learning (FL). The synchronous design relies on strict synchronization among users when executing each FL communication round, while the asynchronous design allows more flexibility...
Preprint
Full-text available
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is Lipschitz continuous, subtracted by a weakly convex function. This type of structured problems has many practical...
Article
Full-text available
Due to its communication efficiency and privacy-preserving capability, federated learning (FL) has emerged as a promising framework for machine learning in 5G-and-beyond wireless networks. Of great interest is the design and optimization of new wireless network structures that support stable and fast operation of FL. Cell-free massive multiple-inpu...
Preprint
Full-text available
This letter considers the development of transmission strategies for the downlink of massive multiple-input multiple-output networks, with the objective of minimizing the completion time of the transmission. Specifically, we introduce a session-based scheme that splits time into sessions and allocates different rates in different sessions for the d...
Article
Full-text available
This letter considers the development of transmission strategies for the downlink of massive multiple-input multiple-output networks, with the objective of minimizing the completion time of the transmission. Specifically, we introduce a session-based scheme that splits time into sessions and allocates different rates in different sessions for the d...
Conference Paper
Full-text available
Graph Augmentation Learning (GAL) provides outstanding solutions for graph learning in handling incomplete data, noise data, etc. Numerous GAL methods have been proposed for graph-based applications such as social network analysis and traffic flow forecasting. However, the underlying reasons for the effectiveness of these GAL methods are still uncl...
Preprint
Full-text available
Graph Augmentation Learning (GAL) provides outstanding solutions for graph learning in handling incomplete data, noise data, etc. Numerous GAL methods have been proposed for graph-based applications such as social network analysis and traffic flow forecasting. However, the underlying reasons for the effectiveness of these GAL methods are still uncl...
Preprint
Full-text available
In this paper, we are interested in studying the asymptotic behavior of the solutions of differential inclusions governed by maximally monotone operators. In the case where the LaSalle's invariance principle is inconclusive, we provide a refined version of the invariance principle theorem. This result derives from the problem of locating the ω−limi...
Article
Full-text available
We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically investigated, in particular, the stability under relaxations, convex combinations and compositions. We derive conical averagedness properties o...
Preprint
Full-text available
Future wireless networks require the integration of machine learning with communications, in an energy-efficient and privacy-preserving manner. Finding energy-efficient designs for federated learning (FL)-enabled wireless networks is of great interest. This work first proposes novel synchronous, asynchronous, and session-based designs for energy-ef...
Conference Paper
Full-text available
With its privacy preservation and communication efficiency, federated learning (FL) has emerged as a learning framework that suits beyond 5G and towards 6G systems. This work looks into a future scenario in which there are multiple groups with different learning purposes and participating in different FL processes. We give energy-efficient solution...
Article
In this paper, we consider a broad class of nonsmooth and nonconvex fractional programs, which encompass many important modern optimization problems arising from diverse areas such as the recently proposed scale-invariant sparse signal reconstruction problem in signal processing. We propose a proximal subgradient algorithm with extrapolations for s...
Article
Full-text available
Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and backward steps involve the operators implicitly via their resolvents. In this paper, we study an adaptive splitting algorithm for finding a zero of the s...
Article
Full-text available
Every maximally monotone operator can be associated with a family of convex functions, called the Fitzpatrick family or family of representative functions. Surprisingly, in 2017, Burachik and Martínez-Legaz showed that the well-known Bregman distance is a particular case of a general family of distances, each one induced by a specific maximally mon...
Preprint
Full-text available
With its privacy preservation and communication efficiency, federated learning (FL) has emerged as a learning framework that suits beyond 5G and towards 6G systems. This work looks into a future scenario in which there are multiple groups with different learning purposes and participating in different FL processes. We give energy-efficient solution...
Article
Full-text available
We introduce a reformulation technique that converts a many-set feasibility problem into an equivalent two-set problem. This technique involves reformulating the original feasibility problem by replacing a pair of its constraint sets with their intersection, before applying Pierra’s classical product space reformulation. The step of combining the t...
Article
Infrastructure-to-vehicle (I2V) and vehicle-to-vehicle (V2V) communications are often combined to extend the connectivity and coverage in the Intelligent Transportation System (ITS) and its applications, e.g., augmented reality, real-time parking management and online shopping. Through multi-hop I2V and V2V communications, requesting vehicles are a...
Conference Paper
Full-text available
Straggler effect is the main bottleneck in realizing federated learning (FL) in wireless networks. This work proposes a novel user (UE) selection approach to mitigate this effect with UE sampling in cell-free massive multiple-input multiple-output networks. Our proposed approach selects only a small subset of UEs for participating in one FL process...
Preprint
Full-text available
Splitting algorithms for finding a zero of sum of operators often involve multiple steps which are referred to as forward or backward steps. Forward steps are the explicit use of the operators and backward steps involve the operators implicitly via their resolvents. In this paper, we study an adaptive splitting algorithm for finding a zero of the s...
Preprint
Full-text available
Every maximally monotone operator can be associated with a family of convex functions, called the Fitzpatrick family or family of representative functions. Surprisingly, in 2017, Burachik and Mart\'inez-Legaz showed that the well-known Bregman distance is a particular case of a general family of distances, each one induced by a specific maximally m...
Preprint
Full-text available
Federated multi-task learning (FMTL) has emerged as a natural choice to capture the statistical diversity among the clients in federated learning. To unleash the potential of FMTL beyond statistical diversity, we formulate a new FMTL problem FedU using Laplacian regularization, which can explicitly leverage relationships among the clients for multi...
Preprint
Full-text available
In this paper, we consider a class of nonsmooth and nonconvex sum-of-ratios fractional optimization problems with block structure. This model class encompasses a broad spectrum of nonsmooth optimization problems such as the energy efficiency maximization problem and the sparse generalized eigenvalue problem. We first show that these problems can be...
Article
In automotive infotainment systems, vehicles using the applications are serviced via continuous infrastructure-to-vehicle (I2V) communications. Additionally, the I2V communications can be combined with vehicle-to-vehicle (V2V) connectivity owing to the small area covered by road side units (RSUs). However, dozens of vehicles have to compete for lim...
Article
Full-text available
Automotive infotainment systems are expected to be first deployed on highways to service drivers travelling long distances, who are more likely to utilize the infotainment applications. In order to meet the stringent requirements of the infotainment systems, road side units (RSUs) are installed along the highway to facilitate a continuous vehicle-t...
Preprint
Full-text available
This work proposes UE selection approaches to mitigate the straggler effect for federated learning (FL) on cell-free massive multiple-input multiple-output networks. To show how these approaches work, we consider a general FL framework with UE sampling, and aim to minimize the FL training time in this framework. Here, training updates are (S1) broa...
Preprint
Full-text available
This work proposes UE selection approaches to mitigate the straggler effect for federated learning (FL) on cell-free massive multiple-input multiple-output networks. To show how these approaches work, we consider a general FL framework with UE sampling, and aim to minimize the FL training time in this framework. Here, training updates are (S1) broa...
Article
Full-text available
We propose a flexible approach for computing the resolvent of the sum of weakly monotone operators in real Hilbert spaces. This relies on splitting methods where strong convergence is guaranteed. We also prove linear convergence under Lipschitz continuity assumption. The approach is then applied to computing the proximity operator of the sum of wea...
Preprint
Full-text available
We introduce a reformulation technique that converts a many-set feasibility problem into an equivalent two-set problem. The reformulation can be viewed as a variant of Pierra's classical product space decomposition which reduces the dimension of the product space by replacing a pair of constraint sets with their intersection. We refer to this as th...
Article
Full-text available
This paper proposes a novel scheme for cell-free massive multiple-input multiple-output (CFmMIMO) networks to support any federated learning (FL) framework. This scheme allows each instead of all the iterations of the FL framework to happen in a large-scale coherence time to guarantee a stable operation of an FL process. To show how to optimize the...
Preprint
Full-text available
In this paper, we consider a broad class of nonsmooth and nonconvex fractional program where the numerator can be written as the sum of a continuously differentiable convex function whose gradient is Lipschitz continuous and a proper lower semicontinuous (possibly) nonconvex function, and the denominator is weakly convex over the constraint set. Th...
Article
Full-text available
This paper studies the joint optimization of precoding, transmit power and data rate allocation for energy-efficient full-duplex (FD) cloud radio access networks (C-RANs). A new nonconvex problem is formulated, where the ratio of total sum rate to total power consumption is maximized, subject to the maximum transmit powers of remote radio heads and...
Article
Full-text available
This paper studies the joint optimization of precoding, transmit power and data rate allocation for energy-efficient full-duplex (FD) cloud radio access networks (C-RANs). A new nonconvex problem is formulated, where the ratio of total sum rate to total power consumption is maximized, subject to the maximum transmit powers of remote radio heads and...
Article
Full-text available
This paper proposes a novel scheme for cell-free massive multiple-input multiple-output (CFmMIMO) networks to support any federated learning (FL) framework. This scheme allows each instead of all the iterations of the FL framework to happen in a large-scale coherence time to guarantee a stable operation of an FL process. To show how to optimize the...
Preprint
Full-text available
In this paper, we consider a conical extension of averaged nonexpansive operators and its usefulness in the convergence analysis of fixed point algorithms. Various properties of conically averaged operators are systematically studied, in particular, the stability under relaxations, convex combinations, and compositions. We then derive the conical a...
Article
The Douglas--Rachford algorithm is a classical and powerful splitting method for minimizing the sum of two convex functions and, more generally, finding a zero of the sum of two maximally monotone operators. Although this algorithm is well understood when the involved operators are monotone or strongly monotone, the convergence theory for weakly mo...
Preprint
Full-text available
Recently, a new distance has been introduced for the graphs of two point-to-set operators, one of which is maximally monotone. When both operators are the subdifferential of a proper lower semicontinuous convex function, this distance specializes under modest assumptions to the classical Bregman distance. We name this new distance the generalized B...
Article
Full-text available
The Douglas--Rachford algorithm is a popular algorithm for solving both convex and nonconvex feasibility problems. While its behaviour is settled in the convex inconsistent case, the general nonconvex inconsistent case is far from being fully understood. In this paper, we focus on the most simple nonconvex inconsistent case: when one set is a hyper...
Article
Full-text available
In this paper, we introduce and study a class of structured set-valued operators, which we call union averaged nonexpansive. At each point in their domain, the value of such an operator can be expressed as a finite union of single-valued averaged nonexpansive operators. We investigate various structural properties of the class and show, in particul...
Article
Full-text available
The Douglas-Rachford projection algorithm is an iterative method used to find a point in the intersection of closed constraint sets. The algorithm has been experimentally observed to solve various nonconvex feasibility problems which current theory cannot sufficiently explain. In this paper, we prove convergence of the Douglas-Rachford algorithm in...
Article
Full-text available
Moreau's seminal paper, introducing what is now called the Moreau envelope and the proximity operator (a.k.a. proximal mapping), appeared in 1965. The Moreau envelope of a given convex function provides a regularized version which has additional desirable properties such as differentiability and full domain. Fifty years ago, Attouch proposed to use...
Article
Full-text available
In this paper, we study the generalized Douglas-Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas-Rachford algorithm and the alternating projection algorithm. Specifically, we establish several local linear convergence results for the algorithm in solving feasibility problems with fi...
Preprint
Full-text available
We propose a flexible approach for computing the resolvent of the sum of weakly monotone operators in real Hilbert spaces. This relies on splitting methods where strong convergence is guaranteed. We also prove linear convergence under Lipschitz continuity assumption. The approach is then applied to computing the proximity operator of the sum of wea...
Preprint
Full-text available
The Douglas-Rachford algorithm is a classical and powerful splitting method for minimizing the sum of two convex functions and, more generally, finding a zero of the sum of two maximally monotone operators. Although this algorithm has been well understood when the involved operators are monotone or strongly monotone, the convergence theory for weak...
Article
Full-text available
This paper aims to maximize the spectral and energy efficiencies of a content-centric cloud radio access network (C-RAN), where users requesting the same contents are grouped together. Data are transferred from a central baseband unit to multiple remote radio heads (RRHs) equipped with local caches. The RRHs then send the received data to each grou...
Preprint
Full-text available
In this paper we introduce and study a class of structured set-valued operators which we call union averaged nonexpansive. At each point in their domain, the value of such an operator can be expressed as a finite union of single-valued averaged nonexpansive operators. We investigate various structural properties of the class and show, in particular...
Article
Full-text available
This work aims to maximize the energy efficiency of a downlink cloud radio access network (C-RAN). Here, data is transferred from a baseband unit in the core network to several remote radio heads via a set of edge routers over capacity-limited fronthaul links. The remote radio heads then send the received signals to their users via radio access lin...
Conference Paper
Full-text available
This work aims to maximize the energy efficiency of a downlink cloud radio access network (C-RAN), where data is transferred from a baseband unit in the core network to several remote radio heads via a set of edge routers over capacity-limited fronthaul links. The remote radio heads then send the received signals to their users via radio access lin...
Preprint
Full-text available
The Douglas--Rachford algorithm is a popular algorithm for solving both convex and nonconvex feasibility problems. While its behaviour is settled in the convex inconsistent case, the general nonconvex inconsistent case is far from being fully understood. In this paper, we focus on the most simple nonconvex inconsistent case: when one set is a hyper...
Article
Full-text available
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we study linear convergence of several projection algorithms for systems of finitely many closed sets. The resul...
Preprint
Full-text available
In this paper, we study the generalized Douglas-Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas-Rachford algorithm and the alternating projection algorithm. Specifically, we establish several local linear convergence results for the algorithm in solving feasibility problems with fi...
Preprint
Full-text available
The Douglas-Rachford projection algorithm is an iterative method used to find a point in the intersection of closed constraint sets. The algorithm has been experimentally observed to solve various nonconvex feasibility problems which current theory cannot sufficiently explain. In this paper, we prove convergence of the Douglas-Rachford algorithm in...
Preprint
Full-text available
Moreau's seminal paper, introducing what is now called the Moreau envelope and the proximity operator (also known as the proximal mapping), appeared in 1965. The Moreau envelope of a given convex function provides a regularized version which has additional desirable properties such as differentiability and full domain. Fifty years ago, Attouch prop...
Article
Full-text available
Solving feasibility problems is a central task in mathematics and the applied sciences. One particularly successful method is the Douglas-Rachford algorithm. In this paper, we provide many new conditions sufficient for finite convergence. Numerous examples illustrate our results.
Article
Full-text available
Delamination is a typical failure mode of composite materials caused by weak bonding. It arises when a crack initiates and propagates under a destructive loading. Given the physical law characterizing the properties of the interlayer adhesive between the bonded bodies, we consider the problem of computing the propagation of the crack front and the...
Preprint
Full-text available
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we study linear convergence of several projection algorithms for systems of finitely many closed sets. The resul...
Article
Full-text available
The Douglas-Rachford algorithm is a classical and very successful method for solving optimization and feasibility problems. In this paper, we provide novel conditions sufficient for finite convergence in the context of convex feasibility problems. Our analysis builds upon, and considerably extends, pioneering work by Spingarn. Specifically, we obta...
Preprint
Full-text available
Solving feasibility problems is a central task in mathematics and the applied sciences. One particularly successful method is the Douglas-Rachford algorithm. In this paper, we provide many new conditions sufficient for finite convergence. Numerous examples illustrate our results.
Article
Full-text available
Many iterative methods for solving optimization or feasibility problems have been invented, and often convergence of the iterates to some solution is proven. Under favourable conditions, one might have additional bounds on the distance of the iterate to the solution leading thus to worst case estimates, i.e., how fast the algorithm must converge. E...
Article
Full-text available
The paper develops a nonconvex bundle method based on the downshift mechanism and a proximity control management technique to solve nonconvex nonsmooth constrained optimization problems. We prove its global convergence in the sense of subsequences for both classes of lower-$C^1$ and upper-$C^1$ functions.
Article
Full-text available
The notion of Fej\'er monotonicity has proven to be a fruitful concept in fixed point theory and optimization. In this paper, we present new conditions sufficient for convergence of Fej\'er monotone sequences and we also provide applications to the study of nonexpansive mappings. Various examples illustrate our results.