Search Results (24)

The convergence rate of the augmented Lagrangian method (ALM) for solving the nonlinear semidefinite optimization problem is studied. Under the Jacobian uniqueness conditions, when a multiplier vector $(\pi ,Y)$ and the penalty parameter $\sigma$ are chosen such that $\sigma$ is larger than a threshold ${\sigma }^{*}>0$ and the ratio $\parallel (\pi ,Y)-({\pi }^{*},Y^{*})\parallel /\sigma$ is small enough, it is demonstrated that the convergence rate of the augmented Lagrange method is linear with respect to $\parallel (\pi ,Y)-({\pi }^{*},Y^{*})\parallel$ and the ratio constant is proportional to $1/\sigma$, where $({\pi }^{*},Y^{*})$ is the multiplier corresponding to a local minimizer. Furthermore, by analyzing the second-order derivative of the perturbation function of the nonlinear semidefinite optimization problem, we characterize the rate constant of local linear convergence of the sequence of Lagrange multiplier vectors produced by the augmented Lagrange method. This characterization shows that the sequence of Lagrange multiplier vectors has a Q-linear convergence rate when the sequence of penalty parameters $\left\{{\sigma }_k\right\}$ has an upper bound and the convergence rate is superlinear when $\left\{{\sigma }_k\right\}$ is increasing to infinity. Full article

This study proposes an Index-Based Neural Network (IBNN) framework for the static analysis of truss structures, employing a Lagrangian dual optimization technique grounded in the force method. A truss is a discrete structural system composed of linear members connected to nodes. Despite their geometric simplicity, analysis of large-scale truss systems requires significant computational resources. The proposed model simplifies the input structure and enhances the scalability of the model using member and node indices as inputs instead of spatial coordinates. The IBNN framework approximates member forces and nodal displacements using separate neural networks and incorporates structural equations derived from the force method as mechanics-informed constraints within the loss function. Training was conducted using the Augmented Lagrangian Method (ALM), which improves the convergence stability and learning efficiency through a combination of penalty terms and Lagrange multipliers. The efficiency and accuracy of the framework were numerically validated using various examples, including spatial trusses, square grid-type space frames, lattice domes, and domes exhibiting radial flow characteristics. Multi-index mapping and domain decomposition techniques contribute to enhanced analysis performance, yielding superior prediction accuracy and numerical stability compared to conventional methods. Furthermore, by reflecting the structured and discrete nature of structural problems, the proposed framework demonstrates high potential for integration with next-generation neural network models such as Quantum Neural Networks (QNNs). Full article

Temporal random noise (TRN) in uncooled infrared detectors significantly degrades image quality. Existing denoising techniques primarily address fixed-pattern noise (FPN) and do not effectively mitigate TRN. Therefore, a novel TRN denoising approach based on total variation regularization and low-rank tensor decomposition is proposed. This method effectively suppresses temporal noise by introducing twisted tensors in both horizontal and vertical directions while preserving spatial information in diverse orientations to protect image details and textures. Additionally, the Laplacian operator-based bidirectional twisted tensor truncated nuclear norm (bt-LPTNN), is proposed, which is a norm that automatically assigns weights to different singular values based on their importance. Furthermore, a weighted spatiotemporal total variation regularization method for nonconvex tensor approximation is employed to preserve scene details. To recover spatial domain information lost during tensor estimation, robust principal component analysis is employed, and spatial information is extracted from the noise tensor. The proposed model, bt-LPTVTD, is solved using an augmented Lagrange multiplier algorithm, which outperforms several state-of-the-art algorithms. Compared to some of the latest algorithms, bt-LPTVTD demonstrates improvements across all evaluation metrics. Extensive experiments conducted using complex scenes underscore the strong adaptability and robustness of our algorithm. Full article

Inspired by the wing-flapping action of birds, this study considers the inherent dynamics among vehicle mechanisms to optimize the vehicle’s geometric parameters. The goal is for the vehicle to imitate the wing-flapping action of birds while minimizing energy consumption and the peak torque during flapping. To accomplish this, a dynamics model and an energy consumption model are established for the vehicle drive mechanism, followed by a multi-objective optimization under the boundary conditions of each parameter. Because of the complexity of the model, a mathematical tool that combines the genetic algorithm with the augmented Lagrange multiplier method is adopted in the optimization process. Simulation results show that the optimized energy consumption and peak moments are reduced. The proposed method provides a theoretical basis for designing a reliable flap-winged vehicle with reasonable parameter choices. Full article

Feature extraction plays a vital role in pattern recognition and computer vision. In recent years, low-rank representation (LRR) has been widely used in feature extraction, due to its robustness against noise. However, existing methods often overlook the impact of a well-constructed low-rank coefficient matrix on projection learning. This paper introduces a novel feature extraction method, i.e., robust discriminative non-negative and symmetric low-rank projection learning (RDNSLRP), where a coefficient matrix with better properties, such as low-rank, non-negativity, symmetry and block-diagonal structure, is utilized as a graph matrix for learning the projection matrix. Additionally, a discriminant term is introduced to increase inter-class divergence while decreasing intra-class divergence, thereby extracting more discriminative features. An iterative algorithm for solving the proposed model was designed by using the augmented Lagrange multiplier method, and its convergence and computational complexity were analyzed. Our experimental results on multiple data sets demonstrate the effectiveness and superior image-recognition performance of the proposed method, particularly on data sets with complex intrinsic structures. Furthermore, by investigating the effects of noise corruption and feature dimension, the robustness against noise and the discrimination of the proposed model were further verified. Full article

Environmental quality is a global concern, especially in Gulf Cooperation Council (GCC) countries where abundant mineral resources, economic growth, and globalization have strained the environment through urbanization and resource exploitation. This study examines the impact of globalization (GLOL), urbanization (URBN), natural resource extraction (NRER), institutional quality (INSQ), and foreign direct investment (FDI) on environmental quality in GCC countries from 1999 to 2021. Cross-sectional dependence (CSD) was assessed using the Lagrange Multiplier (LM) and cross-dependence (CD) techniques, and stationarity was confirmed with the Levin–Lin–Chu test. The Augmented Dickey–Fuller (ADF) co-integration test verified long-term relationships, and Pooled Mean Group Autoregressive Distributed Lag (PMG-ARDL) methodology assessed short- and long-term effects. Our findings show that FDI, GLOL, and INSQ have negative long-term impacts on environmental quality, while NRER and URBN are beneficial. In the short term, FDI and INSQ improve green quality, while GLOL, URBN, and NRER have detrimental effects. Policy recommendations include discouraging FDI in non-renewable projects, promoting sustainable FDI, addressing income inequality to improve environmental quality, and investing in urban development to reduce ecological footprints (ECFTs) and enhance environmental quality in GCC countries. Full article

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. Full article

The synthetic aperture radar (SAR) imaging technique for a frequency-modulated continuous wave (FMCW) has attracted wide attention in the field of burden surface profile measurement. However, the imaging data are virtually under-sampled due to the severely restricted scan time, which prevents the antenna being exposed to high temperatures and heavy dust in the blast furnace (BF) for an extended period. In traditional SAR imaging algorithm research, the insufficient accumulation of scattered energy in reconstructing the burden surface profile leads to lower imaging precision, and the harsh smelting increases the probability of distortion in shape detection. In this study, to address these challenges, a novel rotating SAR imaging algorithm based on the constructed mechanical swing radar system is proposed. This algorithm is inspired by the low-rank property of the sampled signal matrix and the sparsity of burden surface profile images. First, the sparse FMCW signal is modeled, and the position transform matrix, calculated according to the BF dimensions, is embedded into the dictionary matrix. Then, the low-rank and sparsity priors are considered and reformulated as split variables in order to establish a convex optimization problem. Lastly, the augmented Lagrange multiplier (ALM) is employed to solve this problem under double constraints, and the imaging results are obtained using the alternating direction method of multipliers (ADMM). The experimental results demonstrate that, in the subsequent shape detection, the root mean square error (RMSE) is 15.38% lower than the previous algorithm and 15.63% lower under low signal-to-noise (SNR) conditions. In both enclosed and harsh environments, the proposed algorithm is able to achieve higher imaging precision even under high noise. It will be further optimized for speed and reliability, with plans to extend its application to 3D measurements in the future. Full article

Network slicing enables the multiplexing of independent logical networks on the same physical network infrastructure to provide different network services for different applications. The resource allocation problem involved in network slicing is typically a decision-making problem, falling within the scope of reinforcement learning. The advantage of adapting to dynamic wireless environments makes reinforcement learning a good candidate for problem solving. In this paper, to tackle the constrained mixed integer nonlinear programming problem in network slicing, we propose an augmented Lagrangian-based soft actor–critic (AL-SAC) algorithm. In this algorithm, a hierarchical action selection network is designed to handle the hybrid action space. More importantly, inspired by the augmented Lagrangian method, both neural networks for Lagrange multipliers and a penalty item are introduced to deal with the constraints. Experiment results show that the proposed AL-SAC algorithm can strictly satisfy the constraints, and achieve better performance than other benchmark algorithms. Full article

An MILP-based distributed energy management for the coordination of networked microgrids is proposed in this paper. Multiple microgrids and the utility grid are coordinated through iteratively adjusted price signals. Based on the price signals received, the microgrid controllers (MCs) and distribution management system (DMS) update their schedules separately. Then, the price signals are updated according to the generation–load mismatch and distributed to MCs and DMS for the next iteration. The iteration continues until the generation–load mismatch is small enough, i.e., the generation and load are balanced under agreed price signals. Through the proposed distributed energy management, various microgrids and the utility grid with different economic, resilient, emission and socio-economic objectives are coordinated with generation–load balance guaranteed and the microgrid customers’ privacy preserved. In particular, a piecewise linearization technique is employed to approximate the augmented Lagrange term in the alternating direction method of multipliers (ADMM) algorithm. Thus, the subproblems are transformed into mixed integer linear programming (MILP) problems and efficiently solved by open-source MILP solvers, which would accelerate the adoption and deployment of microgrids and promote clean energy. The proposed MILP-based distributed energy management is demonstrated through various case studies on a networked microgrids test system with three microgrids. Full article

Infrared dim small target detection is the critical technology in the situational awareness field currently. The detection algorithm of the infrared patch image (IPI) model combined with the total variation term is a recent research hotspot in this field, but there is an obvious staircase effect in target detection, which reduces the detection accuracy to some extent. This paper further investigates the problem of accurate detection of infrared dim small targets and a novel method based on total variation weighted low-rank constraint (TVWLR) is proposed. According to the overlapping edge information of image background structure characteristics, the weights of constraint low-rank items are adaptively determined to effectively suppress the staircase effect and enhance the details. Moreover, an optimization algorithm combined with the augmented Lagrange multiplier method is proposed to solve the established TVWLR model. Finally, the experimental results of multiple sequence images indicate that the proposed algorithm has obvious improvements in detection accuracy, including receiver operating characteristic (ROC) curve, background suppression factor (BSF) and signal-to-clutter ratio gain (SCRG). Furthermore, the proposed method has stronger robustness under complex background conditions such as buildings and trees. Full article

Alternating Direction Method of Multipliers (ADMM) is a widely used machine learning tool in distributed environments. In the paper, we propose an ADMM-based differential privacy learning algorithm (FDP-ADMM) on penalized quantile regression for distributed functional data. The FDP-ADMM algorithm can resist adversary attacks to avoid the possible privacy leakage in distributed networks, which is designed by functional principal analysis, an approximate augmented Lagrange function, ADMM algorithm, and privacy policy via Gaussian mechanism with time-varying variance. It is also a noise-resilient, convergent, and computationally effective distributed learning algorithm, even if for high privacy protection. The theoretical analysis on privacy and convergence guarantees is derived and offers a privacy–utility trade-off: a weaker privacy guarantee would result in better utility. The evaluations on simulation-distributed functional datasets have demonstrated the effectiveness of the FDP-ADMM algorithm even if under high privacy guarantee. Full article

To improve the detection speed for wide-frequency dense signals (WFDSs), a fast minimization algorithm (FMA) was proposed in this study. Firstly, this study modeled the WFDSs and performed a Taylor-series expansion of the sampled model. Secondly, we simplified the sampling model based on the augmented Lagrange multiplier (ALM) method and then calculated the augmented Lagrange function of the sampling model. Finally, according to the alternating minimization strategy, the Lagrange multiplier vector and the sparse block phasor in the function were iterated individually to realize the measurement of the original signal components. The results show that the algorithm improved the analysis accuracy of the WFDS by 35% to 46% on the IEEE C37.118.1a-2014 standard for the wide-frequency noise test, harmonic modulation test, and step-change test, providing a theoretical basis for the development of the P-class phasor measurement unit (PMU). Full article

To eliminate the mixed noise in hyperspectral images (HSIs), three-dimensional total variation (3DTV) regularization has been proven as an efficient tool. However, 3DTV regularization is prone to losing image details in restoration. To resolve this issue, we proposed a novel TV, named spatial domain spectral residual total variation (SSRTV). Considering that there is much residual texture information in spectral variation image, SSRTV first calculates the difference between the pixel values of adjacent bands and then calculates a 2DTV for the residual image. Experimental results demonstrated that the SSRTV regularization term is powerful at changing the structures of noises in an original HSI, thus allowing low-rank techniques to get rid of mixed noises more efficiently without treating them as low-rank features. The global low-rankness and spatial–spectral correlation of HSI is exploited by low-rank Tucker decomposition (LRTD). Moreover, it was demonstrated that the l_2,1 norm is more effective to deal with sparse noise, especially the sample-specific noise such as stripes or deadlines. The augmented Lagrange multiplier (ALM) algorithm was adopted to solve the proposed model. Finally, experimental results with simulated and real data illustrated the validity of the proposed method. The proposed method outperformed state-of-the-art TV-regularized low-rank matrix/tensor decomposition methods in terms of quantitative metrics and visual inspection. Full article

Hyperspectral image (HSI) is easily corrupted by different kinds of noise, such as stripes, dead pixels, impulse noise, Gaussian noise, etc. Due to less consideration of the structural specificity of stripes, many existing HSI denoising methods cannot effectively remove the heavy stripes in mixed noise. In this paper, we classify the noise on HSI into three types: sparse noise, stripe noise, and Gaussian noise. The clean image and different types of noise are treated as independent components. In this way, the image denoising task can be naturally regarded as an image decomposition problem. Thanks to the structural characteristic of stripes and the low-rank property of HSI, we propose to destripe and denoise the HSI by using stripe and spectral low-rank matrix recovery and combine it with the global spatial-spectral TV regularization (SSLR-SSTV). By considering different properties of different HSI ingredients, the proposed method separates the original image from the noise components perfectly. Both simulation and real image denoising experiments demonstrate that the proposed method can achieve a satisfactory denoising result compared with the state-of-the-art methods. Especially, it outperforms the other methods in the task of stripe noise removal visually and quantitatively. Full article