Search Results (58)

A new two-step interior point method for solving linear programs is presented. The technique uses a convex combination of the auxiliary and central points to compute the search direction. To update the central point, we find the best value for step size such that the feasibility condition is held. Since we use the information from the previous iteration to find the search direction, the inverse of the system is evaluated only once every iteration. A detailed empirical evaluation is performed on NETLIB instances, which compares two variants of the approach to the primal-dual log barrier interior point method. Results show that the proposed method is faster. The method reduces the number of iterations and CPU time(s) by $27\%$ and $18\%$, respectively, on NETLIB instances tested compared to the classical interior point algorithm. Full article

We propose a new alternating direction method of multipliers (ADMM) with an optimal parameter for the unilateral obstacle problem. We first use the five-point difference scheme to discretize the problem. Then, we present an augmented Lagrangian by introducing an auxiliary unknown, and an ADMM is applied to the corresponding saddle-point problem. Through eliminating the primal and auxiliary unknowns, a pure dual algorithm is then used. The convergence of the proposed method is analyzed, and a simple strategy is presented for selecting the optimal parameter, with the largest and smallest eigenvalues of the iterative matrix. Several numerical experiments confirm the theoretical findings of this study. Full article

Digital radio frequency memory (DRFM) has emerged as an advanced technique to achieve a range of jamming signals, due to its capability to intercept waveforms within a short time. multiple-input multiple-output (MIMO) radars can transmit agile orthogonal waveform sets for different pulses to combat DRFM-based jamming, where any two groups of waveform sets are also orthogonal. In this article, a group orthogonal waveform optimal design model is formulated in order to combat DRFM-based jamming by flexibly designing waveforms for MIMO radars. Aiming at balancing the intra- and intergroup orthogonal performances, the objective function is defined as the weighted sum of the intra- and intergroup orthogonal performance metrics. To solve the formulated model, in this article, a group orthogonal waveform design algorithm is proposed. Based on a primal-dual-type method and proper relaxations, the proposed algorithm transforms the original problem into a series of simple subproblems. Numerical results demonstrate that the obtained group orthogonal waveforms have the ability to flexibly suppress DRFM-based deceptive jamming, which is not achievable using p-majorization–minimization (p-MM) and primal-dual, two of the most advanced orthogonal waveform design algorithms. Full article

Landslides are common geological hazards that often result in significant casualties and economic losses. Due to their occurrence in complex terrain areas, conventional geophysical techniques face challenges in early detection and warning of landslides. Semi-airborne electromagnetic (SAEM) technology, utilizing unmanned aerial platforms for rapid unmanned remote sensing, can overcome the influence of complex terrain and serve as an effective approach for landslide detection and monitoring. In response to the low computational efficiency of conventional semi-airborne EM 3D forward modeling, this study proposes an efficient forward modeling method. To handle arbitrarily complex topography and geologic structures, the unstructured tetrahedron mesh is adopted to discretize the earth. Based on the vector finite element formula, the Dual–Primal Finite Element Tearing and Interconnecting (FETI-DP) method is further applied to enhance modeling efficiency. It obtains a reduced order subsystem and avoids directly solving huge overall linear equations by converting the entirety problem into the interface problem. We check our algorithm by comparing it with 1D semi-analytical solutions and the conventional finite element method. The numerical experiments reveal that the FETI-DP method utilities less memory and exhibits higher computation efficiency than the conventional methods. Additionally, we compare the electromagnetic responses with the topography model and flat earth model. The comparison results indicate that the effect of topography cannot be ignored. Further, we analyze the characteristic of electromagnetic responses when the thickness of the aquifer changes in a landslide area. We demonstrate the effectiveness of the 3D SAEM method for landslide detection and monitoring. Full article

Image deblurring is a fundamental image processing task, and research for efficient image deblurring methods is still a great challenge. Most of the currently existing methods are focused on TV-based models and regularization term construction; little efforts are paid to model proposal and correlated algorithms for the fidelity term in fractional-order derivative space. In this paper, we propose a novel fractional-order variational model for image deblurring, which can efficiently address three different blur kernels. The objective functional contains a fractional-order gradient fidelity term and a total generalized variation (TGV) regularization term, and it highlights the ability to preserve details and eliminate the staircase effect. To solve the problem efficiently, we provide two numerical algorithms based on the Chambolle-Pock primal-dual method (PD) and the alternating direction method of multipliers (ADMM). A series of experiments show that the proposed method achieves a good balance between detail preservation and deblurring compared with several existing advanced models. Full article

In contemporary healthcare, the prediction and identification of cardiac diseases is crucial. By leveraging the capabilities of Internet of Things (IoT)-enabled devices and Electronic Health Records (EHRs), the healthcare sector can largely benefit to improve patient outcomes by increasing the accuracy of disease prediction. However, protecting data privacy is essential to promote participation and adhere to rules. The suggested methodology combines EHRs with IoT-generated health data to predict heart disease. For its capacity to manage high-dimensional data and choose pertinent features, a soft-margin L1-regularised Support Vector Machine (sSVM) classifier is used. The large-scale sSVM problem is successfully solved using the cluster primal–dual splitting algorithm, which improves computational complexity and scalability. The integration of federated learning provides a cooperative predictive analytics methodology that upholds data privacy. The use of a federated learning framework in this study, with a focus on peer-to-peer applications, is crucial for enabling collaborative predictive modeling while protecting the confidentiality of each participant’s private medical information. Full article

Optimal power flow (OPF) is one of the most widely studied problems in the field of operations research, as it applies to the optimal and efficient operation of the electric power system. Both the problem formulation and solution techniques have attracted significant research interest over the decades. A wide range of OPF problems have been formulated to cater for the various operational objectives of the power system and are mainly expressed either in polar or rectangular voltage coordinates. Many different solution techniques falling into the two main categories of classical/deterministic optimization and heuristic/non-deterministic optimization techniques have been explored in the literature. This study considers the Volt/VAR optimization (VVO) variant of the OPF problem formulated in rectangular voltage coordinates, which is something of a departure from the majority of the studies, which tend to use the polar coordinate formulation. The heuristic particle swarm optimization (PSO) and the classical primal-dual interior-point method (PDIPM) are applied to the solution of the VVO problem and a comparative analysis of the relative performance of the two algorithms for this problem is presented. Four case studies based on the 6-bus, IEEE 14-bus, 30-bus, and 118-bus test systems are presented. The comparative performance analysis reveals that the two algorithms have complementary strengths, when evaluated on the basis of the solution quality and computational efficiency. Particularly, the PSO algorithm achieves greater power loss minimization, whereas the PDIPM exhibits greater speed of convergence (and, thus, better computational efficiency) relative to the PSO algorithm, particularly for higher-dimensional problems. An additional distinguishing characteristic of the proposed solution is that it incorporates the Newton–Raphson load flow computation, also formulated in rectangular voltage coordinates, which adds to the efficiency and effectiveness of the presented solution method. Full article

The fast and reliable processing of medical images is of paramount importance to adequately generate data to feed machine learning algorithms that can prevent and diagnose health issues. Here, different compressed sensing techniques applied to magnetic resonance imaging are benchmarked as a means to reduce the acquisition time spent in the collection of data and signals that form the image. It is shown that by using these techniques, it is possible to reduce the number of signals needed and, therefore, substantially decrease the time to acquire the measurements. To this end, different algorithms are considered and compared: the iterative re-weighted least squares, the iterative soft thresholding algorithm, the iterative hard thresholding algorithm, the primal dual algorithm and the log barrier algorithm. Such algorithms have been implemented in different analysis programs that have been used to perform the reconstruction of the images, and it was found that the iterative soft thresholding algorithm gives the optimal results. It is found that the images obtained with this algorithm have lower quality than the original ones, but in any case, the quality should be good enough to distinguish each body structure and detect any health problems under an expert evaluation and/or statistical analysis. Full article

Knowledge of the relative performance of the well-known sparse and low-rank compressed sensing models with 3D radial quantitative magnetic resonance imaging acquisitions is limited. We use 3D radial T₁ relaxation time mapping data to compare the total variation, low-rank, and Huber penalty function approaches to regularization to provide insights into the relative performance of these image reconstruction models. Simulation and ex vivo specimen data were used to determine the best compressed sensing model as measured by normalized root mean squared error and structural similarity index. The large-scale compressed sensing models were solved by combining a GPU implementation of a preconditioned primal-dual proximal splitting algorithm to provide high-quality T₁ maps within a feasible computation time. The model combining spatial total variation and locally low-rank regularization yielded the best performance, followed closely by the model combining spatial and contrast dimension total variation. Computation times ranged from 2 to 113 min, with the low-rank approaches taking the most time. The differences between the compressed sensing models are not necessarily large, but the overall performance is heavily dependent on the imaged object. Full article

In this paper, a mixed-order image denoising algorithm containing fractional-order and high-order regularization terms is proposed, which effectively suppresses the staircase effect generated by the TV model and its variants while better preserving the edges and details of the image. Adding different regularization penalties in different regions is fundamental to improving the denoising performance of the model. Therefore, a weight selection function is designed using the structure tensor to achieve a more effective selection of regularization terms in different regions. In each iteration, the regularization parameters are adaptively adjusted according to the Morozov discrepancy principle to promote the performance of the algorithm. Based on the primal–dual theory, the original algorithm is improved by using the predictor–corrector scheme to obtain a more accurate approximate solution while ensuring the convergence of the algorithm. The effectiveness of the proposed algorithm is demonstrated through simulation experiments. Full article

This paper proposes an algorithm that provides operational strategies for multiple tethered autonomous underwater vehicle (T-AUV) systems for entanglement-free navigation. T-AUVs can perform underwater tasks under reliable communication and power supply, which is the most substantial benefit of their operation. Thus, if one can overcome the entanglement issues while utilizing multiple tethered vehicles, the potential applications of the system increase including ecosystem exploration, infrastructure inspection, maintenance, search and rescue, underwater construction, and surveillance. In this study, we focus on developing strategies for task allocation, path planning, and scheduling that ensure entanglement-free operations while considering workload balancing among the vehicles. We do not impose restrictions on the size or shape of the vehicles at this stage; our primary focus is on efficient tether management as an initial work on the topic. To achieve entanglement-free navigation, we propose a heuristic based on the primal-dual technique, which enables initial task allocation and path planning while minimizing the maximum travel cost of the vehicles. Although this heuristic often generates sectioned paths due to its workload-balancing nature, we also propose a mixed approach to provide feasible solutions for non-sectioned initial paths. This approach combines entanglement avoidance techniques with time scheduling and sectionalization methods. To evaluate the effectiveness of our algorithm, extensive simulations were conducted with varying problem sizes. The computational results demonstrate the potential of our algorithm to be applied in real-time operations, as it consistently generates reliable solutions within a reasonable time frame. Full article

Energy forecasting based on univariate time series has long been a challenge in energy engineering and has become one of the most popular tasks in data analytics. In order to take advantage of the characteristics of observed data, a partially linear model is proposed based on principal component analysis and support vector machine methods. The principal linear components of the input with lower dimensions are used as the linear part, while the nonlinear part is expressed by the kernel function. The primal-dual method is used to construct the convex optimization problem for the proposed model, and the sequential minimization optimization algorithm is used to train the model with global convergence. The univariate forecasting scheme is designed to forecast the primary energy consumption of the electric power sector of the United States using real-world data sets ranging from January 1973 to January 2020, and the model is compared with eight commonly used machine learning models as well as the linear auto-regressive model. Comprehensive comparisons with multiple evaluation criteria (including 19 metrics) show that the proposed model outperforms all other models in all scenarios of mid-/long-term forecasting, indicating its high potential in primary energy consumption forecasting. Full article

Aero-engine control systems generally adopt centralized or distributed control schemes, in which all or most of the tasks of the control system are mapped to a specific processor for processing. The performance and reliability of this processor have a significant impact on the control system. Based on the aero-engine distributed control system (DCS), we propose a decentralized controller scheme. The characteristic of this scheme is that a network composed of a group of nodes acts as the controller of the system, so that there is no core control processor in the system, and the computation is distributed throughout the entire network. An LQR output feedback control is constructed using system input and output, and the control tasks executed on each node in the decentralized controller are obtained. The constructed LQR output feedback is equivalent to the optimal LQR state feedback. The primal-dual principle is used to tune the parameters of each decentralized controller. The parameter tuning algorithm is simple to calculate, making it conducive for engineering applications. Finally, the proposed scheme was verified by simulation. The simulation results show that a high-precision feedback gain matrix can be obtained with a maximum of eight iterations. The parameter tuning algorithm proposed in this paper converges quickly during the calculation process, and the constructed output feedback scheme achieves equivalent performance to the state feedback scheme, demonstrating the effectiveness of the design scheme proposed in this paper. Full article

Sparse-array synthesis can considerably reduce the number of sensor elements while optimizing the beam-pattern response performance. The sparsity of an array is related to the degrees of freedom of the array elements. A sparse-array method based on iterative convex optimization and a simulated-annealing expanded array is proposed in this paper. This method transforms the sparse-array problem into a minimum l₁ norm problem and obtains the sparse array by solving the convex optimization problem using the primal-dual algorithm. Meanwhile, to improve the degree of freedom, array elements are expanded using stochastic perturbation. According to the simulated-annealing algorithm, the closed array elements are reopened with a specific probability, which is iteratively thinned and expanded. The results show that the proposed method can obtain an extremely sparse array, which is better than that obtained using the existing methods. Full article

In rotated quadratic cone programming problems, we minimize a linear objective function over the intersection of an affine linear manifold with the Cartesian product of rotated quadratic cones. In this paper, we introduce the rotated quadratic cone programming problems as a “self-made” class of optimization problems. Based on our own Euclidean Jordan algebra, we present a glimpse of the duality theory associated with these problems and develop a special-purpose primal–dual interior-point algorithm for solving them. The efficiency of the proposed algorithm is shown by providing some numerical examples. Full article