Search Results (306)

The quest to multiply two large matrices as fast as possible is one that has already intrigued researchers for several decades. However, the ‘optimal’ algorithm for a certain problem size is still not known. The fast matrix multiplication (FMM) problem can be formulated as a non-convex optimization problem—more specifically, as a challenging tensor decomposition problem. In this work, we build upon a state-of-the-art augmented Lagrangian algorithm, which formulates the FMM problem as a constrained least squares problem, by incorporating a new, generalized cyclic symmetric (CS) structure in the decomposition. This structure decreases the number of variables, thereby reducing the large search space and the computational cost per iteration. The constraints are used to find practical solutions, i.e., decompositions with simple coefficients, which yield fast algorithms when implemented in hardware. For the FMM problem, usually a very large number of starting points are necessary to converge to a solution. Extensive numerical experiments for different problem sizes demonstrate that including this structure yields more ‘unique’ practical decompositions for a fixed number of starting points. Uniqueness is defined relative to the known scale and trace invariance transformations that hold for all FMM decompositions. Making it easier to find practical decompositions may lead to the discovery of faster FMM algorithms when used in combination with sufficient computational power. Lastly, we show that the CS structure reduces the cost of multiplying a matrix by itself. Full article

This paper investigates a simultaneous wireless information and power transfer (SWIPT) decode-and-forward (DF) relay network, where a source node transmits data to a destination node through the assistance of multi-hop passive relays. We employ the time-switching (TS) protocol, enabling the relays to harvest energy from the received previous hop signal to support data forwarding. We first prove that the system throughput monotonically increases with the transmit power of the source node. Next, by employing logarithmic transformations, we convert the non-convex problem of obtaining optimal TS ratios at each relay to maximize the system throughput into a convex optimization problem. Comprehensively taking into account the convergence rate, computational complexity per iteration, and robustness, we selected the log barrier method—a type of interior point method—to address this convex optimization problem, along with providing a detailed implementation procedure. The simulation results validate the optimality of the proposed method and demonstrate its applicability to practical communication systems. For instance, the proposed scheme achieves 1437.3 bps throughput at 40 dBm maximum source power in a 2-relay network—278.6% higher than that of the scheme with TS ratio fixed at 0.75 (379.68 bps). On the other hand, it converges within a 1.36 ms computation time for 5 relays, 6 orders of magnitude faster than exhaustive search (1730 s). Full article

Quadratic programming (QP) formulations are widely used in optimal investment portfolio selection, a central problem in financial decision-making. In practice, asset allocation decisions operate at two interconnected levels: the strategic level, which allocates the budget across major asset classes, and the tactical level, which distributes the allocation within each class to individual securities or instruments. This study evaluates the Frank–Wolfe (FW) algorithm as a computationally alternative to a QP formulation implemented in CVXPY and solved using OSQP (CVXPY–OSQP solver) for tactical investment portfolio optimization. By iteratively solving a linear approximation of the convex objective function, FW offers a distinct approach to portfolio construction. A comparative analysis was conducted using a tactical portfolio model with a small number of stock assets, assessing solution similarity, computational running time, and memory usage. The results demonstrate a clear trade-off between the two methods. While FW can produce portfolio weights closely matching those of the CVXPY–OSQP solver at lower and feasible target returns, its solutions differ at higher returns near the limits of the feasible set. However, FW consistently achieved shorter execution times and lower memory consumption. This study quantifies the trade-offs between accuracy and efficiency and identifies opportunities to improve FW’s accuracy through adaptive iteration strategies under more challenging optimization conditions. Full article

With the rapid growth of user service demands, space–air–ground integrated networks (SAGINs) face challenges such as limited resources, complex connectivity, diverse service requirements, and no-fly zone (NFZ) constraints. To address these issues, this paper proposes a joint optimization approach under NFZ constraints, maximizing system utility by simultaneously optimizing user association, unmanned aerial vehicle (UAV) trajectory, and slice resource allocation. Due to the problem’s non-convexity, it is decomposed into three subproblems: user association, UAV trajectory optimization, and slice resource allocation. To solve them efficiently, we design the iterative SAC-MS algorithm, which combines matching game theory for user association, sequential convex approximation (SCA) for UAV trajectory, and soft actor–critic (SAC) reinforcement learning for slice resource allocation. Simulation results show that SAC-MS outperforms TD3-MS, DDPG-MS, DQN-MS, and hard slicing, improving system utility by 10.53%, 13.17%, 31.25%, and 45.38%, respectively. Full article

Content caching and exchange through device-to-device (D2D) communications can offload data from the centralized base station and improve the quality of users’ experience. However, existing studies often overlook the selfish nature of user equipment (UE) and the heterogeneity of content preferences, which limits their practical applicability. In this paper, we propose a novel incentive-driven uncoded caching framework modeled as a Stackelberg game between a base station (BS) and cache-enabled UEs. The BS acts as the leader by determining the unit incentive reward, while UEs jointly optimize their caching strategies as followers. The particular challenge in our formulation is that the uncoded caching decisions make the UEs’ total utility maximization problem into a non-convex integer programming problem. To address this, we map the UEs’ total utility maximization problem into a potential sub-game and design a potential game-based distributed caching (PGDC) algorithm that guarantees convergence to the optimal joint caching strategy. Building on this, we further develop a dynamic iterative algorithm to derive the Stackelberg equilibrium by jointly optimizing the BS’s cost and the total utility of UEs. The simulation results confirm the existence of the Stackelberg Equilibrium and demonstrate that the proposed PGDC algorithm significantly outperforms benchmark caching schemes. Full article

The transfer-efficient power allocation problem for downlink simultaneous wireless information and power transfer (SWIPT) is investigated in massive multiple-input multiple-output (MIMO) systems in this paper. In the considered system, the base station (BS) equipped with a large number of antennas simultaneously transmits information and sends energy signals to multiple information and energy terminals equipped with a single antenna. The aim is to maximize transfer efficiency while meeting quality-of-service (QoS) requirements for all terminals. First, the closed-form expressions of achievable rates for each information terminal and the harvested energy for each energy terminal are obtained. Then, two optimization problems are formulated according to the obtained expressions, with the purpose of maximizing information transfer efficiency (ITE) and energy transfer efficiency (ETE). The maximizations of ITE and ETE are fractional programming problems and are difficult to solve directly. For this reason, the iterative optimization algorithm is proposed to solve the ITE maximization problem by transforming it into a subtractive form and then utilizing a successive convex approximation (SCA) method. Following a similar approach, another iterative optimization algorithm is proposed to solve the ETE maximization problem by transforming it into a subtractive form and then utilizing a linear programming method. Finally, numerical results demonstrate that the two iterative optimization algorithms can achieve good ITE and ETE, and we also reveal the trade-off between them in this work. Full article

The evaluation of synthetic aperture radar (SAR) jamming effectiveness is a primary means to measure the reliability of jamming effects, and it can provide important guidance for the selection of jamming strategies and application of jamming styles. To address problems in traditional evaluation methods for SAR scene deception jamming, namely the simple adoption of native feature parameters, incomprehensive integration for evaluation indicator design, and the inconsideration of resulting jamming detection effects, this paper proposes a SAR scene deceptive jamming evaluation method oriented to jamming detection. First, four profound feature parameters including the brightness change gradient, texture direction contrast degree, edge matching degree, and noise suppression difference index are extracted in terms of visual and non-visual manners, which accurately highlight the differences between jamming and the background. Subsequently, through nonlinear iterative optimization and loss function design, a comprehensive evaluation indicator, i.e., with a convex decomposition is proposed, which can effectively quantify the contribution of each feature parameter and distinguish the differences in jamming concealment under different scenes. Finally, based on the measured and simulated MiniSAR datasets of urban, mountainous, and other complex scenes, a mapping correlation between the SDD and jamming detection rate is established. The evaluation results show that when the SDD is less than 0.4, the jamming is undetectable; when the SDD is greater than 0.4, for every 0.1 increase in the SDD, the jamming detection rate decreases by approximately 0.1. This provides support for the quantification of jamming effects in terms of detection rate in real applications. Full article

The integration of photovoltaic (PV) generation into distribution systems supports decarbonization and cost reduction but introduces challenges for secure and efficient operation due to voltage fluctuations and power flow variability. Traditional centralized optimal power flow (OPF) methods require full system observability and significant computational resources, limiting their real-time applicability in active distribution systems. This paper proposes a deep neural network (DNN)-based OPF control framework designed for active distribution systems with high PV penetration under limited measurement availability. The proposed method leverages offline convex chance-constrained OPF (convex-CCOPF) solutions, generated through iterative simulations across a wide range of PV and load conditions, to train the DNN to approximate optimal control actions, including on-load tap changer (OLTC) positions and inverter reactive power dispatch. To address observability constraints, the DNN is trained using a reduced set of strategically selected measurement points, making it suitable for real-world deployment in distribution systems with sparse sensing infrastructure. The effectiveness of the proposed framework is validated on the IEEE 33-bus test system under varying operating conditions. The simulation results demonstrate that the DNN achieves near-optimal performance with a significantly reduced computation time compared to conventional OPF solvers while maintaining voltage profiles within permissible limits and minimizing power losses. Full article

High-fidelity finite element analysis (FEA) plays a key role in structural engineering by enabling accurate simulation of displacement, stress, and internal forces under static loads. However, its high computational cost limits applicability in real-time control, iterative design, and large-scale uncertainty quantification. Surrogate modeling provides a computationally efficient alternative by learning input–output mappings from precomputed simulations. Yet, the performance of individual surrogates is often sensitive to data distribution and model assumptions. To enhance both accuracy and robustness, we propose a model averaging framework based on Jackknife Model Averaging (JMA) that integrates six surrogate models: polynomial response surfaces (PRSs), support vector regression (SVR), radial basis function (RBF) interpolation, eXtreme Gradient Boosting (XGB), Light Gradient Boosting Machine (LGBM), and Random Forest (RF). Three ensembles are formed: JMA1 (classical models), JMA2 (tree-based models), and JMA3 (all models). JMA assigns optimal convex weights using cross-validated out-of-fold errors without a meta-learner. We evaluate the framework on the Static Analysis Dataset with over 300,000 FEA simulations. Results show that JMA consistently outperforms individual models in root mean squared error, mean absolute error, and the coefficient of determination, while also producing tighter, better-calibrated conformal prediction intervals. These findings support JMA as an effective tool for surrogate-based structural analysis. Full article

Radar jamming resource allocation is crucial for maximizing jamming effectiveness and ensuring operational superiority in complex electromagnetic environments. However, the existing approaches still sufferfrom inefficiency, instability, and suboptimal global solutions. To address these issues, this work proposes addressing effective jamming resource allocation in dynamic radar countermeasures with multiple jamming types. A deep reinforcement learning framework is designed to jointly optimize transceiver strategies for adaptive jamming under state-switching scenarios. In this framework, a hybrid policy network is proposed to coordinate beam selection and power allocation, while a dynamic fusion metric is integrated to evaluate jamming effectiveness. Then the non-convex optimization is resolved via a proximal policy optimization version 2 (PPO2)-driven iterative algorithm. Experiments demonstrate that the proposed method achieves superior convergence speed and reduced power consumption compared to baseline methods, ensuring robust jamming performance against eavesdroppers under stringent resource constraints. Full article

This paper proposes a novel Guidance and Control architecture for close-range rendezvous and final approach of a chaser spacecraft towards a non-cooperative and tumbling space target. In both phases, reference trajectory generation relies on a Sequential Convex Programming algorithm which iteratively solves a non-linear optimization problem accounting for propellant consumption, relative dynamics, collision avoidance and navigation sensor pointing constraints. At close range, trajectory tracking is entrusted to a translational H-infinity controller, coupled with a quaternion-feed-back regulator for target pointing. In the final approach phase, an attitude-pointing strategy is adopted, requiring a six degree-of-freedom H-infinity controller to follow a reference roto-translational trajectory generated to ensure target-chaser motion synchronization. Performance is evaluated in a high-fidelity simulation environment that includes environmental perturbations, navigation errors, and actuator (i.e., cold gas thrusters and reaction wheels) modelling. In particular, the latter aspects are also addressed by integrating the proposed solution within a complete Guidance, Navigation and Control pipeline including a state-of-the-art LIDAR-based relative navigation filter and a dispatching function for the distribution of commanded control actions to the actuation system. A statistical analysis on 1000 simulations shows the robustness of the proposed approach, achieving centimeter-level position accuracy and sub-degree attitude accuracy near the docking/berthing point. Full article

The Tree–Seed Algorithm (TSA) is a symmetry-driven metaheuristic algorithm that shows potential for complex optimization problems, but it suffers from local optimum entrapment and slow convergence. To address these limitations, we propose the ADTSA algorithm. First, ADTSA adopts a symmetry-driven dual-layer framework for seed generation, which promotes effective information exchange between subpopulations and accelerates convergence speed. In later iterations, ADTSA enhances the population’s exploitation ability through a population fusion mechanism, further improving the convergence speed. Moreover, we propose a historical optimal solution archiving and replacement mechanism, along with a t-distribution perturbation mechanism, to enhance the algorithm’s ability to escape local optima. ADTSA also strengthens population diversity and avoids local optima through convex lens symmetric reverse generation based on the optimal solution. With these mechanisms, ADTSA converges more effectively to the global optimum during the evolutionary process. Tests on the IEEE CEC 2014 benchmark functions showed that ADTSA outperformed several top-performing algorithms, such as LSHADE, JADE, LSHADE-RSP, and the latest TSA variants, and it also excelled in comparison with other optimization algorithms, including GWO, PSO, BOA, GA, and RSA, underscoring its robust performance across diverse testing scenarios. The proposed ADTSA’s applicability in solving complex constrained problems was also validated, with the results showing that ADTSA achieved the best solutions for these complex problems. Full article

Non-orthogonal multiple access (NOMA) technology can effectively improve spectrum efficiency, unmanned aerial vehicle (UAV) communication has the advantage of flexible deployment, and reconfigurable intelligent surface (RIS) can intelligently control the wireless transmission environment. Traditional communication systems have problems such as limited coverage and low spectrum efficiency in complex scenarios. However, a key challenge in deploying RIS-assisted NOMA-UAV communication systems lies in how to jointly optimize the UAV flight trajectory, power allocation strategy, and RIS phase offset to achieve the maximum average achievable rate for users. The non-convex nature of the optimization complicates the problem, making it challenging to find an efficient solution. Based on this, this paper presents a RIS-assisted NOMA-UAV communication system consisting of one UAV, one RIS, and two ground users. To achieve the maximum average rate for users, the UAV flight trajectory, power allocation strategy, and RIS phase offset are jointly optimized. For the non-convex problem, we decompose it into three sub-problems based on its inherent structural characteristics and use an alternating iterative approach to gradually converge to a feasible solution. The simulation results demonstrate that the proposed scheme offers significant advantages in the application scenario. Compared to other benchmark schemes, it delivers superior performance improvements to the communication system and offers higher practical value. Full article

This paper investigated the issues of unstable data collection links and low efficiency in IoT data collection for smart cities by combining active STAR-RIS with UAVs to enhance channel quality, achieving efficient data collection in complex environments. To this end, we propose an active simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-assisted UAV-enabled NOMA data collection system that jointly optimizes active STAR-RIS beamforming, SN power allocation, and UAV trajectory to maximize the system energy efficiency (EE) and the data complete collection rate (DCCR). We apply block coordinate ascent (BCA) to decompose the non-convex problem into three alternating subproblems: combined beamforming optimization of phase shift and amplification gain matrices, power allocation, and trajectory optimization, which are iteratively processed through successive convex approximation (SCA) and fractional programming (FP) methods, respectively. Simulation results demonstrate the proposed algorithm’s rapid convergence and significant advantages over conventional NOMA and OMA schemes in both throughput rate and DCCR. Full article

In this paper, we aim to develop an efficient algorithm for the solving Tensor Robust Principal Component Analysis (TRPCA) problem, which focuses on obtaining a low-rank approximation of a tensor by separating sparse and impulse noise. A common approach is to minimize the convex surrogate of the tensor rank by shrinking its singular values. Due to the existence of various definitions of tensor ranks and their corresponding convex surrogates, numerous studies have explored optimal solutions under different formulations. However, many of these approaches suffer from computational inefficiency primarily due to the repeated use of tensor singular value decomposition in each iteration. To address this issue, we propose a novel TRPCA algorithm that introduces a new convex relaxation for the tensor norm and computes low-rank approximation more efficiently. Specifically, we adopt the tensor average rank and tensor nuclear norm, and further relax the tensor nuclear norm into a sum of the tensor Frobenius norms of the factor tensors. By alternating updates of the truncated factor tensors, our algorithm achieves efficient use of computational resources. Experimental results demonstrate that our algorithm achieves significantly faster performance than existing reference methods known for efficient computation while maintaining high accuracy in recovering low-rank tensors for applications such as color image recovery and background subtraction. Full article