Non-convex Optimization Problem Research Articles

Joint Base Station Selection and Power Allocation Design for Reconfigurable Intelligent Surface-Aided Cell-Free Networks

Cell-free (CF) networks can reduce cell boundaries by densely deploying base stations (BSs) with additional hardware costs and power sources. Integrating a reconfigurable intelligent surface (RIS) into CF networks can cost-effectively increase the capacity and coverage of future wireless systems. This paper considers an RIS-aided CF system where each user is supported by a devoted RIS and can establish connections with multiple BSs for coherent transmission. Specifically, each RIS can enhance signal transmission between users and their selected BSs through passive beam-forming, but also randomly scattered signals from other non-selected BSs to users, causing additional signals and interference in the network. To gain insights into the system performance, we first derive the average signal-to-interference-plus-noise ratio (SINR) received by each user in a closed-form expression. Subsequently, we formulate an optimization problem aimed at maximizing the weighted sum-SINR of all users in the RIS-CF network. This optimization considers both BS transmit power allocation and BS selections as variables to be jointly optimized. To tackle the complexity of this nonconvex optimization problem, we develop an innovative two-layer iterative approach that offers both efficiency and efficacy. This algorithm iteratively updates the transmit power allocation and BS selections to converge to a locally optimal solution. Numerical results demonstrate significant performance improvement for the RIS-CF network using our proposed scheme. These results also highlight the effectiveness of jointly optimizing BS transmit power allocation and BS selections in the RIS-CF network.

A Reentry Trajectory Planning Algorithm via Pseudo-Spectral Convexification and Method of Multipliers

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem, and it constitutes a critical challenge within the field of aerospace engineering. In this paper, an improved sequential convexification algorithm is proposed to solve it and achieve online trajectory planning. In the proposed algorithm, the Chebyshev pseudo-spectral method with high-accuracy approximation performance is first employed to discretize the continuous dynamic equations. Subsequently, based on the multipliers and linearization methods, the original nonconvex trajectory planning problem is transformed into a series of relaxed convex subproblems in the form of an augmented Lagrange function. Then, the interior point method is utilized to iteratively solve the relaxed convex subproblem until the expected convergence precision is achieved. The convex-optimization-based and multipliers methods guarantee the promotion of fast convergence precision, making it suitable for online trajectory planning applications. Finally, numerical simulations are conducted to verify the performance of the proposed algorithm. The simulation results show that the algorithm possesses better convergence performance, and the solution time can reach the level of seconds, which is more than 97% less than nonlinear programming algorithms, such as the sequential quadratic programming algorithm.

Adaptive Dataset Management Scheme for Lightweight Federated Learning in Mobile Edge Computing.

Federated learning (FL) in mobile edge computing has emerged as a promising machine-learning paradigm in the Internet of Things, enabling distributed training without exposing private data. It allows multiple mobile devices (MDs) to collaboratively create a global model. FL not only addresses the issue of private data exposure but also alleviates the burden on a centralized server, which is common in conventional centralized learning. However, a critical issue in FL is the imposed computing for local training on multiple MDs, which often have limited computing capabilities. This limitation poses a challenge for MDs to actively contribute to the training process. To tackle this problem, this paper proposes an adaptive dataset management (ADM) scheme, aiming to reduce the burden of local training on MDs. Through an empirical study on the influence of dataset size on accuracy improvement over communication rounds, we confirm that the amount of dataset has a reduced impact on accuracy gain. Based on this finding, we introduce a discount factor that represents the reduced impact of the size of the dataset on the accuracy gain over communication rounds. To address the ADM problem, which involves determining how much the dataset should be reduced over classes while considering both the proposed discounting factor and Kullback-Leibler divergence (KLD), a theoretical framework is presented. The ADM problem is a non-convex optimization problem. To solve it, we propose a greedy-based heuristic algorithm that determines a suboptimal solution with low complexity. Simulation results demonstrate that our proposed scheme effectively alleviates the training burden on MDs while maintaining acceptable training accuracy.

Reentry trajectory planning for hypersonic vehicles via an improved sequential convex programming method

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem. The solution efficiency and convergence properties of the planning algorithm become an essential point when considering the practical application scenarios. In this paper, an augmented-Lagrange-based improved sequential convex programming algorithm is proposed to solve it and achieve superior solutions with higher accuracy and efficiency. Firstly, the mapped Chebyshev pseudo-spectral method is utilized to convert the continuous optimal control problem into a highly approximately discretized one. In this framework, the discretization technique is employed to discretize the states and control variables at the time interval, which leads to the improvement of ill-conditioned differential matrix and better approximation properties of the variables. Moreover, by introducing slack variables, automatically updated penalty parameters and Lagrange multipliers during the convexification processing, the original nonconvex problem is transformed into an augmented-Lagrange-function-formed relaxed convex one. Then, the arrived convex subproblem can be solved iteratively by the matured interior-point method until the predetermined precision is satisfied. Based on this transformation, it can effectively alleviate the numerical difficulty and improve the convergence property of the proposed improved sequential convex programming algorithm. Finally, Rigorous theoretical analysis is conducted to prove that the solution sequence generated by the proposed algorithm could converge to an approximate global solution of the original problem. Numerical simulations are also presented, and it is demonstrated that the solution time of the proposed algorithm is more than 95% less than that of the traditional nonlinear programming methods without losing the merits of high precision.

Joint beamforming and power splitting design for MISO downlink communication with SWIPT: a comparison between cell-free massive MIMO and small-cell deployments

Simultaneous wireless information and power transfer (SWIPT) has been advocated as a highly promising technology for enhancing the capabilities of 5G and 6G devices. However, the challenge of dealing with large propagation path loss poses a significant hurdle. To address this issue, massive multiple-input multiple-output (MIMO) is employed to enhance the efficiency of SWIPT in cellular-based networks with multiple small cells, and especially increase the energy for cell-edge users. In addition, by leveraging a large set of spatially distributed base stations to collaboratively serve SWIPT-enabled user equipment, the cell-free massive MIMO has the potential to provide even better performance than the conventional small-cell systems. In this work, we extend the investigation to include the application of SWIPT technology with alternating current (AC) logic in the cell-free networks and the small-cell networks and propose joint beamforming and power splitting optimization frameworks to maximize the system sum-rate, subject to the constraints on harvested energy, AC logic energy supply, and total transmit power. The optimization problem is shown to be non-convex, posing a significant challenge. To address this challenge, we resort to a two-stage decomposition approach. Specifically, we first introduce quadratic transform-based fractional programming (FP) algorithms to iteratively solve the non-convex optimization problems in the first stage, achieving near-optimal solutions with low time complexities. To further reduce the complexities, we also incorporate conventional schemes such as zero forcing, maximum ratio transmission, and signal-to-leakage-and-noise ratio for the design of beamforming vectors. Second, to determine the optimal power splitting ratio within the framework, we develop a one-dimensional (1-D) search algorithm to tackle the single variable optimization problem reduced in the second stage. These algorithms are then evaluated in the context of cell-free MIMO and small-cell networks with numerical experiments. The results show that the FP-based algorithms can consistently outperform those utilizing the conventional beamforming schemes, and the solutions of this work can achieve up to fivefold improvement in the system sum-rate than the small-cell counterpart while providing different but comparable performance trends in energy harvesting (EH).

Fluorescence molecular tomography based on an online maximum a posteriori estimation algorithm

Fluorescence molecular tomography (FMT) is a non-invasive, radiation-free, and highly sensitive optical molecular imaging technique for early tumor detection. However, inadequate measurement information along with significant scattering of near-infrared light within the tissue leads to high ill-posedness in the inverse problem of FMT. To improve the quality and efficiency of FMT reconstruction, we build a reconstruction model based on log-sum regularization and introduce an online maximum a posteriori estimation (OPE) algorithm to solve the non-convex optimization problem. The OPE algorithm approximates a stationary point by evaluating the gradient of the objective function at each iteration, and its notable strength lies in the remarkable speed of convergence. The results of simulations and experiments demonstrate that the OPE algorithm ensures good reconstruction quality and exhibits outstanding performance in terms of reconstruction efficiency.

A class of accelerated GADMM-based method for multi-block nonconvex optimization problems

A class of accelerated GADMM-based method for multi-block nonconvex optimization problems

Energy-Efficient Access Point Selection Scheme for Reconfigurable-Intelligent-Surface-Assisted Cell-Free Massive MIMO Systems

Reconfigurable intelligent surface (RIS)-assisted cell-free (CF) massive Multiple-Input Multiple-Output (MIMO) technology exhibits significant potential in enhancing the energy efficiency of 6G mobile communications. Nevertheless, recent studies suggest that both access points (APs) and RISs encounter challenges related to a high energy consumption during operation. To address this issue, strategies involving AP hibernation and RIS shut-off are proposed. Subsequently, an optimization problem is formulated to jointly optimize RISs, beamforming vectors, and AP selection with the aim of maximizing the energy efficiency (EE). Initially, the non-convex optimization problem for maximizing energy efficiency is decomposed into three sub-problems. These sub-problems are subsequently reformulated using fractional programming and variational programming techniques and then solved using the successive convex approximation (SCA) algorithm, Dinkelbach algorithm, and greedy algorithm, respectively. Subsequently, an alternate optimization algorithm based on block gradient descent is introduced to iteratively solve the four-variable optimization problem, thereby obtaining an approximate solution to the original problem. The simulation results demonstrate that the algorithm significantly reduces energy consumption. Specifically, compared to the scheme without the hibernation strategy, the energy efficiency (EE) is enhanced by 35%.

Distributed management of energy communities using stochastic profile steering

This paper presents a novel approach for distributed management of energy communities. The proposed method utilizes a stochastic profile steering algorithm as a greedy heuristic. The optimization process considers random parameters such as local forecasted demand, photovoltaic (PV) production, and the initial energy of electric vehicles (EVs) as embedded scenarios. Profile steering coordinates the flexible electricity assets within an energy community by determining the contribution of each prosumer’s profile to the average value of the objective function. It iteratively selects the prosumer that contributes the most until no further improvements can be made. This process scales linearly with the number of controllable prosumers and can achieve various community-level objectives, such as maximizing self-sufficiency or minimizing aggregated cost-of-energy, even when dealing with non-convex optimization problems for modeling each prosumer’s local energy management system. The outcome of the proposed method optimizes the average value of the community’s objective while ensuring that grid limitations are met within a specified probability. The proposed method is evaluated through simulations involving small-scale communities (5 households) and large-scale communities (100 households). The results demonstrate the efficiency, flexibility, and scalability of the proposed method, as well as its ability to reschedule the aggregated demand to ensure that grid limits are not violated with at least a 95% probability.

Sum rate maximization for RIS-assisted NOMA-enabled underlay AmBC-CR networks

Ambient backscatter communications (AmBC) have introduced a revolutionary approach to wireless communication that utilizes ambient radio frequency (RF) signals in contrast to self-generated RF signals. This makes AmBC a compelling candidate for future Internet-of-Things (IoT) applications, particularly considering the constraints of energy and spectrum resources. In this work, we investigate a cognitive radio (CR) based underlay network of backscatter devices (BDs) that communicate with the backscatter receiver (BR) by utilizing non-orthogonal multiple access (NOMA). Due to the dual fading effect in backscatter networks, the backscatter link is weakened which degrades the achievable performance. In order to tackle this issue, reconfigurable intelligent surface (RIS) is exploited in such networks. Therefore, to maximize the sum rate of the RIS-assisted NOMA-enabled underlay AmBC-CR (RIS-NUAC) network, subject to individual BDs’ data rate constraint and primary receiver (PR) interference threshold constraint, we jointly optimize the phase shift matrix (PSM) at the RIS and the power reflection coefficients (PRCs) at the BDs. To solve the resultant non-convex optimization problem, we propose a sub-optimal solution based on an alternating optimization (AO) algorithm by applying semidefinite relaxation (SDR) and rank one approximation. Based on simulation results, the proposed scheme demonstrates superior performance over baseline schemes, including NOMA with random phases, NOMA without RIS, orthogonal multiple access (OMA) with optimal phases, and OMA without RIS.

Golden jackal optimization for economic load dispatch problems with complex constraints

This research paper uses the golden jackal optimization (GJO), a novel meta-heuristic algorithm, to address power system economic load dispatch (ELD) problems. The GJO emulates the hunting behavior of golden jackals. GJO algorithm uses the cooperative attacking behavior of golden jackals to tackle complicated optimization problems efficaciously. The objective of ELD problem is to distribute power system load requirement to the different generators with a minimum total fuel cost of generation. ELD problems are highly complex, non-linear, and non-convex optimization problems while considering constraints namely valve point loading effect (VPL) and prohibited operating zones (POZs). The proposed GJO algorithm is applied to solve complex, non-linear, and non-convex ELD problems. Six different test systems having 6, 10, 13, 40, and 140 generators with various constraints are used to validate the usefulness of the suggested GJO method. Simulation outcomes of the test system are compared with various algorithms reported in the algorithms such as particle swarm optimization (PSO), ant colony optimization (ACO), and backtracking search algorithm (BSA). Results show that the proposed GJO algorithm produces minimal fuel cost and has good convergence in solving ELD problems of power system engineering.

Scan-Free and Fully Automatic Tracking of Native Knee Anatomy from Dynamic Stereo-Radiography with Statistical Shape and Intensity Models.

Kinematic tracking of native anatomy from stereo-radiography provides a quantitative basis for evaluating human movement. Conventional tracking procedures require significant manual effort and call for acquisition and annotation of subject-specific volumetric medical images. The current work introduces a framework for fully automatic tracking of native knee anatomy from dynamic stereo-radiography which forgoes reliance on volumetric scans. The method consists of three computational steps. First, captured radiographs are annotated with segmentation maps and anatomic landmarks using a convolutional neural network. Next, a non-convex polynomial optimization problem formulated from annotated landmarks is solved to acquire preliminary anatomy and pose estimates. Finally, a global optimization routine is performed for concurrent refinement of anatomy and pose. An objective function is maximized which quantifies similarities between masked radiographs and digitally reconstructed radiographs produced from statistical shape and intensity models. The proposed framework was evaluated against manually tracked trials comprising dynamic activities, and additional frames capturing a static knee phantom. Experiments revealed anatomic surface errors routinely below 1.0 mm in both evaluation cohorts. Median absolute errors of individual bone pose estimates were below 1.0 or mm for 15 out of 18 degrees of freedom in both evaluation cohorts. Results indicate that accurate pose estimation of native anatomy from stereo-radiography may be performed with significantly reduced manual effort, and without reliance on volumetric scans.

Accelerated analysis on the triple momentum method for a two-layer ReLU neural network

The momentum method has become the workhorse in the deep learning community. To theoretical understand its success, researchers put efforts in demystifying its convergence properties when optimizing neural networks. For the convex problem, it is well-known that the triple momentum (TM) method owns the fastest theoretical convergence rate among all first-order methods. However, there exists no theoretical convergence results about the TM method in solving the non-convex neural networks training problem, let alone its acceleration guarantee. In this paper, we focus on the training process of the TM method for a two-layer ReLU neural network. Inspired by the accurate characterization of the high-resolution dynamical system, we consider the high-resolution ordinary differential equation (ODE) of the TM method. Under the over-parameterized assumption, we derive that the original non-convex optimization problem can be transformed to a strongly convex task. By applying an appropriate Lyapunov function, we prove that the TM method can linearly converge to a global minimum. Compared to the heavy ball method and Nesterov’s accelerated gradient method, our result provides the first guarantee for the acceleration of the TM method in training neural networks. Through empirical experiments, the accelerated convergence of the TM method and the effect of over-parameterization are validated.

Efficient economic operation based on load dispatch of power systems using a leader white shark optimization algorithm

This article proposes the use of a leader white shark optimizer (LWSO) with the aim of improving the exploitation of the conventional white shark optimizer (WSO) and solving the economic operation-based load dispatch (ELD) problem. The ELD problem is a crucial aspect of power system operation, involving the allocation of power generation resources to meet the demand while minimizing operational costs. The proposed approach aims to enhance the performance and efficiency of the WSO by introducing a leadership mechanism within the optimization process, which aids in more effectively navigating the complex ELD solution space. The LWSO achieves increased exploitation by utilizing a leader-based mutation selection throughout each generation of white sharks. The efficacy of the proposed algorithm is tested on 13 engineer benchmarks non-convex optimization problems from CEC 2020 and compared with recent metaheuristic algorithms such as dung beetle optimizer (DBO), conventional WSO, fox optimizer (FOX), and moth-flame optimization (MFO) algorithms. The LWSO is also used to address the ELD problem in different case studies (6 units, 10 units, 11 units, and 40 units), with 20 separate runs using the proposed LWSO and other competitive algorithms being statistically assessed to demonstrate its effectiveness. The results show that the LWSO outperforms other metaheuristic algorithms, achieving the best solution for the benchmarks and the minimum fuel cost for the ELD problem. Additionally, statistical tests are conducted to validate the competitiveness of the LWSO algorithm.

Network sum-rate maximization for network-coded clustered uplink NOMA networks with SWIPT-enabled relays

This paper considers network sum-rate maximization for network-coded clustered uplink non-orthogonal multiple-access (NOMA) networks with simultaneous wireless information and power transfer (SWIPT)-enabled relays. Specifically, the aim is to perform joint power allocation, power-splitting, and relay selection (J-PA-PS-RS), subject to quality-of-service (QoS) requirements. The formulated problem is excessively computationally-intensive, as it is a non-convex optimization problem. To efficiently solve it, it is split into two sub-problems: (1) joint power allocation and power-splitting per relay, and (2) relay selection. Particularly, a solution procedure is proposed, where the joint user and relay power allocation, and power-splitting per relay sub-problem is solved via a low-complexity iterative three-layer algorithm, and then followed by optimal relay selection. Simulation results have revealed that the proposed solution procedure can efficiently be used to maximize the network sum-rate, achieve near-optimal solutions, and outperform other benchmark schemes, while satisfying QoS constraints.

Phase-only beampattern synthesis for maximizing mainlobe gain via Riemannian Newton method

Beampattern synthesis with phase-only weights is extensively utilized in phased-array systems due to the virtue of low-cost and high power efficiency. It is always a non-convex optimization problem having constant modulus constraints (CMCs) and the performance significantly depends on the employed solvers. This paper discusses the phase-only beampattern synthesis for maximizing the mainlobe gain with the constraints on the mainlobe ripple and the relative sidelobe level. As CMC is equivalent to a complex circle manifold, the proposed beampattern synthesis is considered as a manifold optimization problem, and then decomposed into several subproblems under the framework of manifold alternating direction method of multipliers (ADMM). In particular, the subproblem for updating phase-only weights is efficiently tackled by a second-order Riemannian Newton method, which has faster convergence speed and no requirement on line search compared to widely-used first-order Riemannian manifold methods. The explicit convergence condition is derived and the computational complexity is also analyzed. Numerical results show that the proposed method has better performance on the mainlobe gain and sidelobe control accuracy, or less computational cost compared to several representative approaches, such as convex relaxation, standard ADMM, Riemannian gradient descent-based ADMM and Riemannian conjugate gradient methods.

Mitigation of total harmonic distortion and flicker emission in the presence of harmonic loads by optimal siting and sizing of wind turbines and energy storage systems

In distribution networks (DNs), there are significant technical challenges due to the high penetration of renewable energy resources (RERs), especially wind turbines (WTs) and the presence of non-linear electrical loads. One of the most important challenges is power quality. In such networks, to mitigate flicker emission produced by WTs and network voltage harmonics, it is necessary to solve the planning problems considering power quality objectives and standards. For this aim, this paper attempts to improve DN performance by optimal siting and sizing of WTs and energy storage systems (ESSs). In the planning problem, to take into account the power quality issue, flicker emission, total harmonic distortion (THD), and network voltage deviation (NVD) are included in the optimization problem. To effectively solve the planning problem, which is a non-linear and non-convex optimization problem, three variants of genetic algorithm (GA) are used. Simulation results indicate that optimal sizing and siting of WTs not only significantly improve the power quality issue but also improves the network performance.

Interference Situational Aware Beam Pointing Optimization for Dense LEO Satellite Communication System

Recently, the low earth orbit (LEO) mega-constellation faces serious time-varying interferences due to spectrum sharing, dense deployment, and high mobility. Therefore, it is important to study the interference avoidance techniques for the dense LEO satellite system. In this paper, the interference situational aware beam pointing optimization technique is proposed. Firstly, the angle of departure (AoD) and angle of arrival (AoA) of the interfering links are obtained to represent the time-varying interference. Then, the interference avoidance problem for dense LEO satellite systems is modeled as a non-convex optimization problem, and a particle swarm optimization (PSO) based method is proposed to obtain the optimal beam pointing of the user terminal (UT). Simulations show that the relative error of the mean signal-to-interference plus noise ratio (SINR) obtained by the proposed method is 0.51%, so the co-channel interference can be effectively mitigated for the dense LEO satellite communication system.

DF-ParPINN: parallel PINN based on velocity potential field division and single time slice focus

Modified Benney-Luke equation (mBL equation) is a three-dimensional temporal-spatial equation with complex structures, that is a high-dimensional partial differential equation (PDE), it is also a new equation of the physical ocean field, and its solution is important for studying the internal wave-wave interaction of inclined seafloor. For conventional PDE solvers such as the pseudo-spectral method, it is difficult to solve mBL equation with both accuracy and speed. Physics-informed neural network (PINN) incorporates physical prior knowledge in deep neural networks, which can solve PDE with relative accuracy and speed. However, PINN is only suitable for solving low-dimensional PDE with simple structures, and not suitable for solving high-dimensional PDE with complex structures. This is mainly because high-dimensional PDEs usually have complex structures and high-order derivatives and are likely to be high-dimensional non-convex functions, and the high-dimensional non-convex optimization problem is an NP-hard problem, resulting in the PINN easily falling into inaccurate local optimal solutions when solving high-dimensional PDEs. Therefore, we improve the PINN for the characteristics of mBL equation and propose “DF-ParPINN: parallel PINN based on velocity potential field division and single time slice focus” to solve mBL equation with large amounts of data. DF-ParPINN consists of three modules: temporal-spatial division module of overall velocity potential field, data rational selection module of multiple time slices, and parallel computation module of high-velocity fields and low-velocity fields. The experimental results show that the solution time of DF-ParPINN is no more than 0.5s, and its accuracy is much higher than that of PINN, PIRNN, cPINN, and DeepONet. Moreover, the relative error of DF-ParPINN after deep training 1000000 epochs can be reduced to less than 0.1. The validity of DF-ParPINN proves that the improved PINN also can solve high dimensional PDE with complex structures and large amounts of data quickly and accurately, which is of great significance to the deep learning of the physical ocean field.

Enhancing efficiency and reliability of multi-energy systems: A hybrid heuristic algorithm for interconnected energy hubs

In response to the escalating demand for sustainable energy solutions, the integration of diverse energy sources has gained prominence. Energy hubs, facilitating the amalgamation of multiple sources, enhance system efficiency and flexibility. Yet, coordinating the operation of such multi-energy systems remains challenging due to complexity and uncertainties, especially with renewable sources. This paper introduces a Cournot model-based approach for optimizing three interconnected energy hubs. The objective is to minimize total operating costs while ensuring reliability and efficiency. Leveraging the Cournot model, commonly employed in energy studies for competition and pricing, we capture the strategic behavior of energy hubs. The proposed solution employs a modified butterfly flame heuristic algorithm to navigate the non-linear and non-convex optimization problem, efficiently seeking global optimal solutions. Numerical experiments on a three-hub test case validate the method, demonstrating a 3.5 % reduction in total operation costs compared to the base case and over 2.5 % cost reduction for each hub. The proposed algorithm outperforms traditional methods in terms of convergence speed and solution quality, offering a promising avenue for optimizing the operation and management of multi-energy systems. In summary, this paper introduces a novel approach grounded in the Cournot model and a hybrid heuristic algorithm for optimizing three interconnected energy hubs, effectively addressing uncertainties associated with renewable sources and ensuring reliable and efficient system operation.