Showing papers on "Convex optimization published in 2021"

Simultaneously Transmitting And Reflecting (STAR) RIS Aided Wireless Communications

Abstract: The novel concept of simultaneously transmitting and reflecting (STAR) reconfigurable intelligent surfaces (RISs) is investigated, where the incident wireless signal is divided into transmitted and reflected signals passing into both sides of the space surrounding the surface, thus facilitating a full-space manipulation of signal propagation. Based on the introduced basic signal model of ‘STAR’, three practical operating protocols for STAR-RISs are proposed, namely energy splitting (ES), mode switching (MS), and time switching (TS). Moreover, a STAR-RIS aided downlink communication system is considered for both unicast and multicast transmission, where a multi-antenna base station (BS) sends information to two users, i.e., one on each side of the STAR-RIS. A power consumption minimization problem for the joint optimization of the active beamforming at the BS and the passive transmission and reflection beamforming at the STAR-RIS is formulated for each of the proposed operating protocols, subject to communication rate constraints of the users. For ES, the resulting highly-coupled non-convex optimization problem is solved by an iterative algorithm, which exploits the penalty method and successive convex approximation. Then, the proposed penalty-based iterative algorithm is extended to solve the mixed-integer non-convex optimization problem for MS. For TS, the optimization problem is decomposed into two subproblems, which can be consecutively solved using state-of-the-art algorithms and convex optimization techniques. Finally, our numerical results reveal that: 1) the TS and ES operating protocols are generally preferable for unicast and multicast transmission, respectively; and 2) the required power consumption for both scenarios is significantly reduced by employing the proposed STAR-RIS instead of conventional reflecting/transmiting-only RISs.

Optimization-Based Collision Avoidance

Abstract: This article presents a novel method for exactly reformulating nondifferentiable collision avoidance constraints into smooth, differentiable constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid obstacles while moving in an $n$ -dimensional space. The proposed reformulation is exact, does not introduce any approximations, and applies to general obstacles and controlled objects that can be represented as the union of convex sets. We connect our results with the notion of signed distance, which is widely used in traditional trajectory generation algorithms. Our method can be applied to generic navigation and trajectory planning tasks, and the smoothness property allows the use of general-purpose gradient- and Hessian-based optimization algorithms. Finally, in case a collision cannot be avoided, our framework allows us to find “least-intrusive” trajectories, measured in terms of penetration. We demonstrate the efficacy of our framework on an automated parking problem, where our numerical experiments suggest that the proposed method is robust and enables real-time optimization-based trajectory planning in tight environments. Sample code of our example is provided at https://github.com/XiaojingGeorgeZhang/OBCA .

Push–Pull Gradient Methods for Distributed Optimization in Networks

Abstract: In this article, we focus on solving a distributed convex optimization problem in a network, where each agent has its own convex cost function and the goal is to minimize the sum of the agents’ cost functions while obeying the network connectivity structure. In order to minimize the sum of the cost functions, we consider new distributed gradient-based methods where each node maintains two estimates, namely an estimate of the optimal decision variable and an estimate of the gradient for the average of the agents’ objective functions. From the viewpoint of an agent, the information about the gradients is pushed to the neighbors, whereas the information about the decision variable is pulled from the neighbors, hence giving the name “push–pull gradient methods.” The methods utilize two different graphs for the information exchange among agents and, as such, unify the algorithms with different types of distributed architecture, including decentralized (peer to peer), centralized (master–slave), and semicentralized (leader–follower) architectures. We show that the proposed algorithms and their many variants converge linearly for strongly convex and smooth objective functions over a network (possibly with unidirectional data links) in both synchronous and asynchronous random-gossip settings. In particular, under the random-gossip setting, “push–pull” is the first class of algorithms for distributed optimization over directed graphs. Moreover, we numerically evaluate our proposed algorithms in both scenarios, and show that they outperform other existing linearly convergent schemes, especially for ill-conditioned problems and networks that are not well balanced.

Observer-based Sliding Mode Control for Networked Fuzzy Singularly Perturbed Systems Under Weighted Try-Once-Discard Protocol

Abstract: In this paper, the sliding mode control issue is investigated for a class of discrete-time Takagi-Sugeno fuzzy networked singularly perturbed systems via an observer-based technique. Moreover, to process the measurement output and schedule the transmission sequence for eliminating the communication burden, a logarithmic quantizer and a weighted try-once-discard protocol are synthesized, which can further improve the network bandwidth utilization in networked control systems. Based on the fuzzy observer states, a novel fuzzy sliding surface is established with taking the singularly perturbed parameter into consideration properly, and we endeavor to synthesize a fuzzy observer-based sliding mode control law such that the reachability of the prescribed sliding surface could be guaranteed. In addition, by virtue of the convex optimization theory and Lyapunov approach, sufficient conditions are developed to guarantee the asymptotic stability of the sliding mode dynamics as well as the error system with an expected $H_{\infty }$ performance. Finally, a verification example is presented to illustrate the feasibility and effectiveness of the proposed method.

Federated Learning Over Wireless Networks: Convergence Analysis and Resource Allocation

Abstract: There is an increasing interest in a fast-growing machine learning technique called Federated Learning (FL), in which the model training is distributed over mobile user equipment (UEs), exploiting UEs’ local computation and training data. Despite its advantages such as preserving data privacy, FL still has challenges of heterogeneity across UEs’ data and physical resources. To address these challenges, we first propose FEDL , a FL algorithm which can handle heterogeneous UE data without further assumptions except strongly convex and smooth loss functions. We provide a convergence rate characterizing the trade-off between local computation rounds of each UE to update its local model and global communication rounds to update the FL global model. We then employ FEDL in wireless networks as a resource allocation optimization problem that captures the trade-off between FEDL convergence wall clock time and energy consumption of UEs with heterogeneous computing and power resources. Even though the wireless resource allocation problem of FEDL is non-convex, we exploit this problem’s structure to decompose it into three sub-problems and analyze their closed-form solutions as well as insights into problem design. Finally, we empirically evaluate the convergence of FEDL with PyTorch experiments, and provide extensive numerical results for the wireless resource allocation sub-problems. Experimental results show that FEDL outperforms the vanilla FedAvg algorithm in terms of convergence rate and test accuracy in various settings.

Implementable tensor methods in unconstrained convex optimization.

Abstract: In this paper we develop new tensor methods for unconstrained convex optimization, which solve at each iteration an auxiliary problem of minimizing convex multivariate polynomial. We analyze the simplest scheme, based on minimization of a regularized local model of the objective function, and its accelerated version obtained in the framework of estimating sequences. Their rates of convergence are compared with the worst-case lower complexity bounds for corresponding problem classes. Finally, for the third-order methods, we suggest an efficient technique for solving the auxiliary problem, which is based on the recently developed relative smoothness condition (Bauschke et al. in Math Oper Res 42:330–348, 2017; Lu et al. in SIOPT 28(1):333–354, 2018). With this elaboration, the third-order methods become implementable and very fast. The rate of convergence in terms of the function value for the accelerated third-order scheme reaches the level $$O\left( {1 \over k^4}\right) $$ , where k is the number of iterations. This is very close to the lower bound of the order $$O\left( {1 \over k^5}\right) $$ , which is also justified in this paper. At the same time, in many important cases the computational cost of one iteration of this method remains on the level typical for the second-order methods.

Lower complexity bounds of first-order methods for convex-concave bilinear saddle-point problems

Abstract: On solving a convex-concave bilinear saddle-point problem (SPP), there have been many works studying the complexity results of first-order methods. These results are all about upper complexity bounds, which can determine at most how many iterations would guarantee a solution of desired accuracy. In this paper, we pursue the opposite direction by deriving lower complexity bounds of first-order methods on large-scale SPPs. Our results apply to the methods whose iterates are in the linear span of past first-order information, as well as more general methods that produce their iterates in an arbitrary manner based on first-order information. We first work on the affinely constrained smooth convex optimization that is a special case of SPP. Different from gradient method on unconstrained problems, we show that first-order methods on affinely constrained problems generally cannot be accelerated from the known convergence rate O(1 / t) to $$O(1/t^2)$$ , and in addition, O(1 / t) is optimal for convex problems. Moreover, we prove that for strongly convex problems, $$O(1/t^2)$$ is the best possible convergence rate, while it is known that gradient methods can have linear convergence on unconstrained problems. Then we extend these results to general SPPs. It turns out that our lower complexity bounds match with several established upper complexity bounds in the literature, and thus they are tight and indicate the optimality of several existing first-order methods.

Distributed stochastic gradient tracking methods

Abstract: In this paper, we study the problem of distributed multi-agent optimization over a network, where each agent possesses a local cost function that is smooth and strongly convex. The global objective is to find a common solution that minimizes the average of all cost functions. Assuming agents only have access to unbiased estimates of the gradients of their local cost functions, we consider a distributed stochastic gradient tracking method (DSGT) and a gossip-like stochastic gradient tracking method (GSGT). We show that, in expectation, the iterates generated by each agent are attracted to a neighborhood of the optimal solution, where they accumulate exponentially fast (under a constant stepsize choice). Under DSGT, the limiting (expected) error bounds on the distance of the iterates from the optimal solution decrease with the network size n, which is a comparable performance to a centralized stochastic gradient algorithm. Moreover, we show that when the network is well-connected, GSGT incurs lower communication cost than DSGT while maintaining a similar computational cost. Numerical example further demonstrates the effectiveness of the proposed methods.

A dual approach for optimal algorithms in distributed optimization over networks

Abstract: We study dual-based algorithms for distributed convex optimization problems over networks, where the objective is to minimize a sum ∑ i = 1 m f i ( z ) of functions over in a network. We provide co...

Price-Based Resource Allocation for Edge Computing: A Market Equilibrium Approach

Abstract: The emerging edge computing paradigm promises to deliver superior user experience and enable a wide range of Internet of Things (IoT) applications. In this paper, we propose a new market-based framework for efficiently allocating resources of heterogeneous capacity-limited edge nodes (EN) to multiple competing services at the network edge. By properly pricing the geographically distributed ENs, the proposed framework generates a market equilibrium (ME) solution that not only maximizes the edge computing resource utilization but also allocates optimal resource bundles to the services given their budget constraints. When the utility of a service is defined as the maximum revenue that the service can achieve from its resource allotment, the equilibrium can be computed centrally by solving the Eisenberg-Gale (EG) convex program. We further show that the equilibrium allocation is Pareto-optimal and satisfies desired fairness properties including sharing incentive, proportionality, and envy-freeness. Also, two distributed algorithms, which efficiently converge to an ME, are introduced. When each service aims to maximize its net profit (i.e., revenue minus cost) instead of the revenue, we derive a novel convex optimization problem and rigorously prove that its solution is exactly an ME. Extensive numerical results are presented to validate the effectiveness of the proposed techniques.

Confidence Interval Based Distributionally Robust Real-Time Economic Dispatch Approach Considering Wind Power Accommodation Risk

Abstract: This article proposes a confidence interval based distributionally robust real-time economic dispatch (CI-DRED) approach, which considers the risk related to accommodating wind power. In this article, only the wind power curtailment and load shedding due to wind power disturbances are evaluated in the operational risk. The proposed approach can strike a balance between the operational costs and risk even when the wind power probability distribution cannot be precisely estimated. A novel ambiguity set is developed based on the imprecise probability theory, which can be constructed based on the point-wise or family-wise confidence intervals. The worst pair of distributions in the established ambiguity set is then identified, and the original CI-DRED problem is transformed into a determined nonlinear dispatch problem accordingly. By using the sequential convex optimization method and piecewise linear approximation method, the nonlinear dispatch model is reformulated as a mixed integer linear programming problem, for which off-the-shelf solvers are available. A fast inactive constraint filtration method is also applied to further relieve the computational burden. Numerical results on the IEEE 118-bus system and a real 445-bus system verify the effectiveness and efficiency of the proposed approach.

Zeroth-Order Nonconvex Stochastic Optimization: Handling Constraints, High Dimensionality, and Saddle Points

Abstract: In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization, with a focus on addressing constrained optimization, high-dimensional setting, and saddle point avoiding. To handle constrained optimization, we first propose generalizations of the conditional gradient algorithm achieving rates similar to the standard stochastic gradient algorithm using only zeroth-order information. To facilitate zeroth-order optimization in high dimensions, we explore the advantages of structural sparsity assumptions. Specifically, (i) we highlight an implicit regularization phenomenon where the standard stochastic gradient algorithm with zeroth-order information adapts to the sparsity of the problem at hand by just varying the step size and (ii) propose a truncated stochastic gradient algorithm with zeroth-order information, whose rate of convergence depends only poly-logarithmically on the dimensionality. We next focus on avoiding saddle points in nonconvex setting. Toward that, we interpret the Gaussian smoothing technique for estimating gradient based on zeroth-order information as an instantiation of first-order Stein’s identity. Based on this, we provide a novel linear-(in dimension) time estimator of the Hessian matrix of a function using only zeroth-order information, which is based on second-order Stein’s identity. We then provide a zeroth-order variant of cubic regularized Newton method for avoiding saddle points and discuss its rate of convergence to local minima.

Asynchronous Finite-Time Filtering of Markov Jump Nonlinear Systems and Its Applications

Abstract: In this paper, the problem of asynchronous finite-time filtering issue is addressed for a class of Markov jump nonlinear systems with incomplete transition rate. The so-called asynchronization means that the filter’s modes do not synchronize with the system’s modes. Both the stochastic finite-time boundedness (FTBs) problem and the stochastic input–output finite-time stability (IO-FTSy) problem are involved. By resorting to the mode-dependent Lyapunov function approach and the matrix inequality techniques, some interesting results are derived to verify the properties of the stochastic FTBs and the stochastic IO-FTSy of the asynchronous filtering error system. The asynchronous filter parameters can be reduced to the solvability of some convex optimization problems. Finally, a single-link robot arm and a tunnel diode circuit are applied to elucidate the proposed algorithms.

Weighted Sum Secrecy Rate Maximization Using Intelligent Reflecting Surface

Abstract: This paper aims to investigate the benefit of using intelligent reflecting surface (IRS) in multi-user multiple-input single-output (MU-MISO) systems, in the presence of eavesdroppers. We maximize the weighted sum secrecy rate by jointly designing the secure beamforming (BF), the artificial noise (AN), as well as the phase shift of the IRS. An alternating optimization (AO) method is proposed to deal with the formulated non convex problem. In particular, the secure beamforming and AN jamming matrix are optimally designed via the successive convex approximation (SCA) approach for given phase shift, which can be derived by considering the alternating direction method of multiplier (ADMM) and element-wise block coordinate decent (EBCD) methods. Finally, simulation results are presented to show the benefit of the IRS in terms of improving the secrecy performance, when compared to other methods.

Energy-Efficient Federated Edge Learning with Joint Communication and Computation Design

Abstract: This paper studies a federated edge learning system, in which an edge server coordinates a set of edge devices to train a shared machine learning (ML) model based on their locally distributed data samples. During the distributed training, we exploit the joint communication and computation design for improving the system energy efficiency, in which both the communication resource allocation for global ML-parameters aggregation and the computation resource allocation for locally updating ML-parameters are jointly optimized. In particular, we consider two transmission protocols for edge devices to upload ML-parameters to edge server, based on the non-orthogonal multiple access (NOMA) and time division multiple access (TDMA), respectively. Under both protocols, we minimize the total energy consumption at all edge devices over a particular finite training duration subject to a given training accuracy, by jointly optimizing the transmission power and rates at edge devices for uploading ML-parameters and their central processing unit (CPU) frequencies for local update. We propose efficient algorithms to solve the formulated energy minimization problems by using the techniques from convex optimization. Numerical results show that as compared to other benchmark schemes, our proposed joint communication and computation design significantly can improve the energy efficiency of the federated edge learning system, by properly balancing the energy tradeoff between communication and computation.

Fixed Point Strategies in Data Science

Abstract: The goal of this article is to promote the use of fixed point strategies in data science by showing that they provide a simplifying and unifying framework to model, analyze, and solve a great variety of problems. They are seen to constitute a natural environment to explain the behavior of advanced convex optimization methods as well as of recent nonlinear methods in data science which are formulated in terms of paradigms that go beyond minimization concepts and involve constructs such as Nash equilibria or monotone inclusions. We review the pertinent tools of fixed point theory and describe the main state-of-the-art algorithms for provenly convergent fixed point construction. We also incorporate additional ingredients such as stochasticity, block-implementations, and non-Euclidean metrics, which provide further enhancements. Applications to signal and image processing, machine learning, statistics, neural networks, and inverse problems are discussed.

Online Optimization for Networked Distributed Energy Resources With Time-Coupling Constraints

Abstract: This paper proposes a Lyapunov optimization-based online distributed (LOOD) algorithmic framework for active distribution networks (ADNs) with numerous photovoltaic inverters and inverter air conditionings (IACs). In the proposed scheme, ADNs can track an active power setpoint reference at the substation in response to transmission-level requests while concurrently minimizing the social utility loss and ensuring the security of voltages. Conventional distributed optimization methods are rarely feasible to track the optimal solutions in fast variable environments using a fine-grained sampling interval where the underlying optimization problem evolves with the iterations of the algorithms. In contrast, based on the framework of online convex optimization (OCO), the developed approach uses a distributed algebraic update to compute the next round decisions relying on the current feedback of measurements. Notably, the time-coupling constraints of IACs are decoupled for online implementation with Lyapunov optimization technique. An incentive scheme is tailored to coordinate the customer-owned assets in lieu of the direct control from network operators. Optimality and convergency are characterized analytically. Finally, we corroborate the proposed method on a modified version of 33-node test feeder. Benchmark tests show that the proposed method is computationally and economically efficient, and outperforming existing algorithms.

Multi-UAV Deployment for Throughput Maximization in the Presence of Co-Channel Interference

Abstract: Over the past few years, there has been a growing interest in using unmanned aerial vehicles (UAVs) for high-rate wireless communication systems due to their highly flexible deployment and maneuverability. The aim of this article is to propose a 3-D multi-UAV deployment approach to provide Quality-of-Service (QoS) requirements for different types of user distributions in the presence of co-channel interference by maximizing the minimum achievable system throughput for all of the ground users. The proposed approach is divided into two separate algorithms. In the first algorithm, by using the mean-shift technique and prior knowledge of users’ positions provided by the global positioning system (GPS), it has been shown that one can simultaneously find $xy$ coordinates of UAVs, which are associated with the maximum of users’ density and schedule users to UAVs. Once the $xy$ -Cartesian coordinates of UAVs are determined, UAVs’ altitudes and transmit powers are separately optimized. Since these problems are nonconvex optimizations, the successive convex optimization technique has been applied to approximate their nonconvex constraints. In the second algorithm, the block coordinate descent technique is leveraged to jointly optimize UAVs altitudes and transmit powers by tightening the bounds obtained for approximations. It is then proven that the suggested algorithm is guaranteed to converge. The computational complexity of the proposed placement approach is derived. Numerical experiments are carried out to evaluate the performance of our technique and show its superiority to conventional benchmarks.

Decentralized and parallel primal and dual accelerated methods for stochastic convex programming problems

Abstract: Abstract We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles, the proposed methods are optimal in terms of the number of communication steps. However, for all classes of the objective, the optimality in terms of the number of oracle calls per node takes place only up to a logarithmic factor and the notion of smoothness. By using mini-batching technique, we show that the proposed methods with stochastic oracle can be additionally parallelized at each node. The considered algorithms can be applied to many data science problems and inverse problems.

A Dynamic Virtual Machine Placement and Migration Scheme for Data Centers

Abstract: We study the problem of virtual machine (VM) placement and migration in a data center. In the current approaches, VMs are assigned to physical servers using on-demand provisioning. Such an approach is simple but it often results in a poor performance due to resource fragmentation. Additionally, sub-optimal VM placement usually generates unneeded VM migration and unnecessary cross network traffic. The efficiency of a datacenter therefore significantly depends on how VMs are provisioned and where they are placed. A good placement scheme will not only improve the quality of service but also reduce the operation cost of the data center. In this paper, we study the problem of optimal VM placement and migration to minimize resource usage and power consumption in a data center. We formulate the optimization problem as a joint multiple objective function and solve it by leveraging the framework of convex optimization. Due to the intractable nature of the combinatorial optimization, we then propose Multi-level Join VM Placement and Migration (MJPM) algorithms based on the relaxed convex optimization framework to approximate the optimal solution. The theoretical analysis demonstrates the effectiveness of our proposed algorithms that substantially increases data center efficiency. In addition, our extensive simulation results on different practical topologies show significant performance improvement over the existing approaches.

Trajectory Design for UAV-Enabled Multiuser Wireless Power Transfer With Nonlinear Energy Harvesting

Abstract: In this paper, we study an unmanned aerial vehicle (UAV)-enabled multiuser wireless power transfer (WPT) network, where a UAV is responsible for providing wireless energy for a set of ground devices (GDs) deployed in an area. We focus on the design of UAV trajectory subject to the maximum flight speed limit, in order to maximize the minimum harvested energy among GDs over a particular charging duration. Different from prior works that considered simplified linear energy harvesting models, this paper for the first time takes into account the realistic nonlinear energy harvesting model for the UAV trajectory design. However, the formulated trajectory design problem is highly non-convex and has infinite number of variables, thus making it be challenging to be solved optimally. To tackle this difficulty, we adopt the following three-step approach to obtain an efficient solution. First, we rigorously characterize that the optimal trajectory follows a new successive-hover-and-fly (SHF) structure, where the UAV hovers at a certain set of points for efficiently transferring energy, and flies among these hovering points with the maximum speed following certain arcs (not necessarily straight lines). Next, based on this SHF structure, we transform the original problem to a new one for finding a set of turning point variables during the maximum-speed flight, at which the UAV changes the flight direction without hovering. Finally, we use the techniques of convex approximation to solve the transformed problem. According to the convexity of the nonlinear energy harvesting model, we iteratively solve a series of convex optimization problems to update the UAV trajectory towards a high-quality solution. Numerical results show the convergence of the proposed approach, and validate its performance gain over conventional designs.

Scalable Semidefinite Programming

Abstract: Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorith...

l ₂– l ∞ State Estimation for Persistent Dwell-Time Switched Coupled Networks Subject to Round-Robin Protocol

Abstract: This article is concerned with the issue of $l_{2}$ – $l_{\infty }$ state estimation for nonlinear coupled networks, where the variation of coupling mode is governed by a set of switching signals satisfying a persistent dwell-time property. To solve the problem of data collisions in a constrained communication network, the round-robin protocol, as an important scheduling strategy for orchestrating the transmission order of sensor nodes, is introduced. Redundant channels with signal quantization are used to improve the reliability of data transmission. The main purpose is to determine an estimator that can guarantee the exponential stability in mean square sense and an $l_{2}$ – $l_{\infty }$ performance level of the estimation error system. Based on the Lyapunov method, sufficient conditions for the addressed problem are established. The desired estimator gains can be obtained by addressing a convex optimization case. The correctness and availability of the developed approach are finally explained via two illustrative examples.

Joint 3D Trajectory and Power Optimization for UAV-Aided mmWave MIMO-NOMA Networks

Abstract: This paper considers an unmanned aerial vehicle (UAV)-aided millimeter Wave (mmWave) multiple-input-multiple-output (MIMO) non-orthogonal multiple access (NOMA) system, where a UAV serves as a flying base station (BS) to provide wireless access services to a set of Internet of Things (IoT) devices in different clusters. We aim to maximize the downlink sum rate by jointly optimizing the three-dimensional (3D) placement of the UAV, beam pattern and transmit power. To address this problem, we first transform the non-convex problem into a total path loss minimization problem, and hence the optimal 3D placement of the UAV can be achieved via standard convex optimization techniques. Then, the multiobjective evolutionary algorithm based on decomposition (MOEA/D) based algorithm is presented for the shaped-beam pattern synthesis of an antenna array. Finally, by transforming the original problem into an optimal power allocation problem under the fixed 3D placement of the UAV and beam pattern, we derive the closed-form expression of transmit power based on Karush-Kuhn-Tucker (KKT) conditions. In addition, inspired by fraction programming (FP), we propose a FP-based suboptimal algorithm to achieve a near-optimal performance. Numerical results demonstrate that the proposed algorithm achieves a significant performance gain in terms of sum rate for all IoT devices, as compared with orthogonal frequency division multiple access (OFDMA) scheme.

Reliability-Constrained Throughput Optimization of Industrial Wireless Sensor Networks With Energy Harvesting Relay

Abstract: In industrial wireless sensor networks (IWSNs), a lot of energy is wasted in the form of electromagnetic radiations. It can be effectively utilized with energy harvesting (EH), which absorbs part of the energy in the transmission signal but reduces the throughput and reliability of IWSNs. In this article, we study the throughput optimization of IWSNs with EH from the interference radio-frequency (RF) signal considering the reliability constraint of the industrial information transmission. Under the premise of limited energy supply of EH relays, the throughput maximization of IWSNs is formulated as a nonconvex optimization problem. In order to transform the nonconvex problem to a convex optimization problem, the successive convex approximation (SCA) approach is adopted. Furthermore, a power allocation algorithm is designed to maximize the total transmission rate of the network. Simulation results demonstrate that the proposed algorithm can maximize the throughput under the primise of SINR reliability.

Convex Relaxation Methods for Community Detection

Abstract: This paper surveys recent theoretical advances in convex optimization approaches for community detection. We introduce some important theoretical techniques and results for establishing the consistency of convex community detection under various statistical models. In particular, we discuss the basic techniques based on the primal and dual analysis. We also present results that demonstrate several distinctive advantages of convex community detection, including robustness against outlier nodes, consistency under weak assortativity, and adaptivity to heterogeneous degrees. This survey is not intended to be a complete overview of the vast literature on this fast-growing topic. Instead, we aim to provide a big picture of the remarkable recent development in this area and to make the survey accessible to a broad audience. We hope that this expository article can serve as an introductory guide for readers who are interested in using, designing, and analyzing convex relaxation methods in network analysis.

Convex Optimization of Integrated Power-Gas Energy Flow Model With Applications to Probabilistic Energy Flow

Abstract: Energy flow calculation is a fundamental problem of the integrated power and gas system (IPGS) operation and planning. However, the nonlinear gas flow model introduces major challenges to the energy flow calculation. In this paper, we propose a tractably convex optimization model to solve the energy flow problem in IPGSs. It is demonstrated that the proposed optimization model has the same optimal solution as the original nonlinear steady energy flow model. Also, piecewise linearization is adopted to tightly linearize the nonlinear objective function of the model, which transforms the formulated convex optimization into a linear program one. Thus, the computation complexity of the proposed energy flow model is significantly reduced as compared with the existing methods. In addition, the proposed model can be extended to probabilistic energy flow estimation. Extensive case studies are conducted to validate the effectiveness of the proposed energy flow model using three IPGSs.

Intelligent Reflecting Surface Enhanced Secure Transmission Against Both Jamming and Eavesdropping Attacks

Abstract: Both the jammer and the eavesdropper pose severe threat to wireless communications due to the broadcast nature of wireless channels. In this paper, an intelligent reflecting surface (IRS) assisted secure communication system is considered, where a base station (BS) wishes to reliably convey information to a user, in the presence of both a jammer and an eavesdropper whose transmit informations are not completely known. Specifically, with the imperfect third-party node's channel state information (CSI) and no knowledge of the jammer's transmit beamforming, we aim to maximize the system achievable rate by jointly designing the BS's transmit beamforming and the IRS's reflect beamforming, while limiting the information leakage to the potential eavesdropper. Due to the non-convexity and intractability of the original problem induced by the incompleted information, we utilize the auxiliary variables, Cauchy-Schwarz inequality, and General Sign-Definiteness transformation to convert the original optimization problem into a tractable convex optimization problem, and then obtain the high-quality optimal solution by using the successive convex approximation and penalty convex concave procedure. Numerical simulations demonstrate the superiority of our proposed optimization algorithm compared with existing approaches, and also reveal the impact of key parameters on the achievable system performance.