Multiplier Method Research Articles

An Adaptive Alternating Direction Method of Multipliers for Vehicle-to-Everything Computation Offloading in Cloud–Edge Collaborative Environment

An Adaptive Alternating Direction Method of Multipliers for Vehicle-to-Everything Computation Offloading in Cloud–Edge Collaborative Environment

Mixed Finite Element Formulation in Nonlinear Geometrical Analysis of Space Trusses and Application to Trusses With Member Length Imperfection

Abstract Space trusses usually have a significant number of elements. As a result, it is inevitable that some elements have imperfections. In this study, the authors proposed a mixed finite element method for nonlinear geometrical analysis of space trusses. The post-buckling behavior of space trusses with length imperfections was predicted using a code list written in the programming software. The numerical results indicate that when the length imperfection approaches zero, the results converge to those obtained in studies on standard trusses. A second approach based on the displacement model is also proposed, in which the Lagrange multiplier method is used to deal with the member length imperfection. The results show that the two approaches proposed by the authors are effective, in which the mix formulation based on the finite element model is superior to that based on the displacement model. These results verify the accuracy of the method. Based on the proposed method, the effects of imperfections in the element layers on the truss were studied. The results show that the imperfections in the top two element layers have the maximum influence on the limit load value, whereas the remaining layers have a negligible influence. The combination of the imperfect lengths of these two layers of elements can produce results in which the limit load value is much larger than in the case of a perfect system. Based on the obtained results, it is possible to provide a solution for improving the overall stability of truss structures by creating reasonable imperfections.

Self-Adaptive Alternating Direction Method of Multipliers for Image Denoising

In this study, we introduce a novel self-adaptive alternating direction method of multipliers tailored for image denoising. Our approach begins by formulating a collaborative regularization model that upholds structured sparsity within images while delving into spatial correlations among pixels. To address the challenge of penalty parameter influence on convergence speed, we innovate by proposing a self-adaptive alternating direction method of multipliers. This adaptive technique autonomously adjusts variable penalty parameters to expedite algorithm convergence, thereby markedly boosting algorithmic performance. Through a fusion of simulations and empirical analyses, our research demonstrates that this novel methodology significantly amplifies the efficacy of denoising processes.

A novel bearing weak fault diagnosis method based on rank constrained low-rank and sparse decomposition

Abstract Addressing the challenge of diagnosing incipient bearing faults amidst significant noise, a novel diagnostic approach is introduced, leveraging a Rank Constrained Low-Rank and Sparse Decomposition (RCLRSD) model tailored for weak fault detection in bearings. Initially, we raised the Autocorrelation Function of the Square Envelope in Frequency Domain (AFSEFD) as an innovative method for the estimation of fault frequencies. Subsequently, we constructed a two-dimensional observation matrix, which is formulated independently of predefined assumptions. Then, we examine the configuration and distribution patterns of bearing fault signals, uncovering the low-rank nature of fault characteristics within a designated two-dimensional transform domain. Moreover, we found the noise signal to exhibit sparsity and an approximate Gaussian distribution. Based on this, a rank-constrained low-rank sparse decomposition model is established, and rank-constrained low-rank regular constraints for feature information and sparse regular constraints and Gaussian constraints for interference signals are constructed respectively. Ultimately, we employed the Gray Wolf Optimization (GWO) algorithm to refine the model parameters, and we deduced the model's solver via the Alternating Direction Method of Multipliers (ADMM). The proposed RCLRSD model decomposes bearing fault data into three constituents: low-rank, sparse, and Gaussian components, effectively addressing the challenge of extracting weak fault signatures from bearings. The weak feature extraction capability of the RCLRSD model is verified using a multi-interference simulation model and experimental data of bearing failures under strong noise conditions; the generalization of the model is verified by the classification effect of the Support Vector Machine (SVM) under two bearing failure datasets. Comparison with various algorithms confirms the superiority of the proposed algorithm.

Bimodal PET/MRI generative reconstruction based on VAE architectures

Abstract •Objective:In this study, we explore positron emission tomography(PET)/magnetic resonance imaging (MRI) joint reconstruction within a deeplearning (DL) framework, introducing a novel synergistic method.
•Approach:We propose a new approach based on a variational autoencoder (VAE)constraint combined with the alternating direction method of multipliers (ADMM)optimization technique. We compare several VAE architectures, including jointVAE, mixture of experts (MoE) and product of experts (PoE), to determine theoptimal latent representation for the two modalities. We trained then evaluatedthe architectures on a brain PET/MRI dataset.
•Main results:We showed that our approach takes advantage of each modalitysharing information to each other, which results in improved peak signal-to-noiseratio (PSNR) and structural similarity (SSIM) as compared with traditionalreconstruction methods, particularly for short acquisition times. We find that theone particular architecture, MMJSD, is the most effective for our methodology.
•Significance:The proposed method outperforms classical approaches especiallyin noisy and undersampled conditions by making use of the two modalities together to compensate for the missing information

Regulatory Threshold of Soil and Water Conservation Measures on Runoff and Sediment Processes in the Sanchuan River Basin

Research on the runoff and sediment reduction effects of soil and water conservation measures has always been a topic of interest, which is of great significance for carrying out sustainable strategies for soil and water conservation in the Yellow River Basin. This study aims to find the threshold years of soil and water conservation measures for reductions in runoff and sediment. Through the analysis of various soil and water conservation measures, runoff, sediment, and rainfall data in the Sanchuan River Basin from 1960 to 2019, we determined the threshold years of soil and water conservation measures on runoff and sediment processes using the Hydrology and Lagrange Multiplier method. The results are as follows: The trend in flood season rainfall and annual rainfall in the Sanchuan River Basin is consistent. The 1990s was a turning period in the annual rainfall and flood season rainfall of the Sanchuan River Basin. The 2000s was a turning period of the runoff in the Sanchuan River Basin, while the sediment entered a stable period after 2000. The best periods for reducing runoff and sediment were the initial treatment period (1967–1979) and the centralized treatment period (1980–1996). The runoff and sediment reduction effects of each soil and water conservation measure during the initial treatment period (1967–1979) were terrace (32.8%) > dam (30.1%) > grass (18.6%) > forest (18.5%), while their effects during the centralized treatment period (1980–1996) were grass (53.7%) > terrace (20.7%) > dam (14.6%) > forest (11.0%). The runoff and sediment reduction effects of various soil and water conservation measures during different treatment periods indicate that the runoff reduction effect reached its peak in 2003–2005, while the sediment reduction benefit reached its peak in 2013–2015. Based on the comprehensive benefits of runoff and sediment regulation, 2013–2015 are considered to be the threshold years for various soil and water conservation measures, with the measures covering respective average areas of 4.85 × 104, 17.80 × 104, 1.15 × 104, and 0.82 × 104 hm2. These research results will have a certain significance for the reasonable allocation of soil and water conservation measures and sustainable development in the Yellow River Basin.

Analyses for Signal Detection Algorithms and Corresponding VLSI Architectures Applied for Massive MIMO Systems

Abstract. In the field of 5G communications, the utilization of Massive MIMO has significantly improved the spectral efficiency. However, signal detection involves large-scale matrix inversion, which is computationally intensive. Traditional techniques for linear detection, such as Zero Forcing and Minimum Mean Square Error, struggle to effectively reduce computational complexity. Therefore, this paper introduces three methods to mitigate the complexity in signal detection: the Alternating Direction Method of Multipliers for conditions where the base stations quantities are nearly equivalent to the users quantities, the Neumann series expansion method that replaces matrix inversion, and iterative methods that approximate the true value through iterative updates. Future work should focus on optimizing the iterative expressions and incorporating tools such as deep learning to further reduce computational complexity and accurately retrieve the signal values.

Analysis of Serial Foot Radiographs to Determine Foot Height Multipliers.

The multiplier method is an arithmetic calculation that estimates the amount of growth remaining until skeletal maturity. When predicting lower limb length discrepancy, differences in foot height are added to femur and tibia discrepancies. Foot height multipliers have not been calculated using radiographic measurements, so it is unclear whether foot height develops at the same pace as the femur and tibia. This study used serial images to calculate foot height multipliers and compared them to published lower limb and foot length multipliers. The Bolton Brush radiograph collection was used to measure foot height on the lateral foot view. Multipliers were calculated for ages with at least 10 serial study visits. 212 patients (2195 radiographs) were included in the study (102 female, 110 male patients). Foot height multipliers were calculated for ages 0 to 17 years (females) and 0 to 18 years (males). Multipliers decreased with age, but qualitatively plateau at age 13 (females) and age 15 (males). Lower extremity multipliers have a more dramatic growth curve, indicating comparatively greater lower extremity growth after birth. However, when comparing the limb length discrepancy calculation using the lower extremity multiplier versus the foot height multiplier for the foot portion, the difference was negligible. This paper provides a database of foot height multipliers. Foot height seems to grow on a different trajectory than other lower limb components, confirming that one should consider separate multiplier values. The difference created by the foot height multiplier versus the lower extremity multiplier appears to be modest. Separate use of the foot height multiplier may only be necessary for young children with large foot height discrepancies, but further study to confirm the lack of impact of the foot height multiplier on limb length discrepancy calculations is needed. Our data were derived from normal children, so it is unknown if the presence of a talo-calcaneal coalition would affect foot height on the involved side. Level III-retrospective comparative study.

Conservation laws for a perturbed resonant nonlinear Schrödinger equation in quantum fluid dynamics and quantum optics

The current paper retrieves the conservation laws for the extended version of the resonant nonlinear Schrödinger's equation for description of physical processes in quantum fluid dynamics and quantum optics. The method of multipliers recovers three fundamental conservation laws. Analytical solutions of equation are found taking into account traveling wave reduction. The conserved quantities are subsequently computed from the soliton solution of the model equation that is derived in this work too.

Conservation laws, traveling wave solutions and wavelet solution for the two-component Novikov equation

Abstract The objective of this present article is to study the two-component Novikov equation. This
 equation is also known as Geng-Xue equation and is characterized by cubic nonlinearities. By
 applying the multiplier method, new conserved quantities are found, and some traveling wave
 solutions are derived based on the (G′/G )-expansion method. Furthermore, a numerical solution
 is determined by employing the Haar wavelet collocation method. In order to confirm the
 accuracy, this numerical solution is compared with the solution obtained by (G′/G )-expansion
 method. Additionally, the convergence analysis of the Haar wavelet collocation method is also
 presented.

Existence and stability of a weakly damped laminated beam with a nonlinear delay

AbstractA weakly damped laminated beam system with nonlinear time delay is studied. The existence and uniqueness are proved by Faedo–Galerkin approach. We prove that the system is stable under some specific conditions on the weight of the delay and the equal wave speeds of propagation. The general energy decay rate is established by using multiplier method and some properties of convex functions. This decay result is obtained without imposing any restrictive growth assumption on the damping term at the origin. In addition, our result improves and develops some existing results in the literature.

Cooperative energy and reserve trading strategies for multiple integrated energy systems based on asymmetric nash bargaining theory

To tackle the issues of cooperative energy and reserve trading as well as fair cooperative benefit allocation among multiple integrated energy systems (IESs), this paper proposes a two-stage cooperative energy and reserve trading model for multiple integrated energy systems (MIESs). Specifically, at day-ahead stage, MIESs aim to maximize their overall profit through cooperative electricity and heat trading. At real-time stage, MIESs trade demand response (DR) reserve to minimize the overall wind power deviation compensation cost. To reduce the complexity in model solution, we transform the model into two sub-problems. In sub-problem 1, we determine the energy and DR reserve trading volumes. Here, distributionally robust optimization (DRO) is utilized to manage the severe uncertainties in wind power distribution. In sub-problem 2, based on the outcomes from sub-problem 1, we settle the energy and DR reserve trading prices. To ensure the fairness of benefit allocation, asymmetric Nash bargaining theory is applied to assess each IES's contributions in trading volumes and profit growth. Interval adaptive alternating direction method of multipliers (IA-ADMM) is used to preserve each IES's privacy. Finally, simulation results demonstrate that, compared with independent operation, cooperative trading among MIESs increases profits for all IESs, thereby motivating their participation in cooperative trading.

Unified algorithms for distributed regularized linear regression model

In recent years, distributed statistical models have received increasing attention for large-scale data analysis. On the one hand, data sets come from multiple data sources, and are stored in different locations due to limited bandwidth and storage, or privacy protocols, directly centralizing all data together is impossible. On the other hand, the size of data is so large that it is difficult or inefficient to analyze data together. There are two main research aspects to using distributed statistical models to analyze large-scale data. The first one is to study the statistical convergence rate under some mild assumptions. The second one is to establish fast and efficient optimization algorithms considering the property of the loss function. There is a lot of research on the first aspect, but relatively little research on the second one. Motivated by this, we consider the construction of unified algorithms for distributed linear regression with different losses and regularizers. As a result, we designed two type methods, proximal alternating direction method of multipliers (pADMM) and distributed accelerated proximal gradient method with line-search (DAPGL). In order to demonstrate the efficiency of the proposed algorithms, we perform numerical experiments on the distributed Huber-Lasso model and Huber-Group-Lasso model. In view of the numerical results, we can observe that these two algorithms are more competitive than some of state-of-art algorithms. In particular, DAPGL algorithm performs better than pADMM in most cases.

Robust mixed-order graph learning for incomplete multi-view clustering

Incomplete multi-view clustering (IMVC) aims to address the clustering problem of multi-view data with partially missing samples and has received widespread attention in recent years. Most existing IMVC methods still have the following issues that require to be further addressed. They focus solely on the first-order correlation information among samples, neglecting the more intricate high-order connections. Additionally, these methods always overlook the noise or inaccuracies in the similarity matrix. To address above issues, a novel method named Robust Mixed-order Graph Learning (RMoGL) is proposed for IMVC. Specifically, to enhance the robustness to noise, the similarity matrices are separated into clean graphs and noise graphs. To capture complex high-order relationships among samples, the dynamic high-order similarity graphs are innovatively constructed from the recovered data. The clean graphs are endowed with mixed-order information and tend towards to obtain a consensus graph via a self-weighted manner. An efficient algorithm based on Alternating Direction Method of Multipliers (ADMM) is designed to solve the proposed RMoGL, and superior performance is demonstrated by compared with nine state-of-the-art methods across eight datasets. The source code of this work is available at https://github.com/guowei1314/RMoGL.

Simultaneous image denoising and completion through convolutional sparse representation and nonlocal self-similarity

Low rank matrix approximation (LRMA) has been widely studied due to its capability of approximating original image from the degraded image. According to the characteristics of degraded images, image denoising and image completion have become research objects. Existing methods are usually designed for a single task. In this paper, focusing on the task of simultaneous image denoising and completion, we propose a weighted low rank sparse representation model and the corresponding efficient algorithm based on LRMA. The proposed method integrates convolutional analysis sparse representation (ASR) and nonlocal statistical modeling to maintain local smoothness and nonlocal self-similarity (NLSM) of natural images. More importantly, we explore the alternating direction method of multipliers (ADMM) to solve the above inverse problem efficiently due to the complexity of simultaneous image denoising and completion. We conduct experiments on image completion for partial random samples and mask removal with different noise levels. Extensive experiments on four datasets, i.e., Set12, Kodak, McMaster, and CBSD68, show that the proposed method prevents the transmission of noise while completing images and has achieved better quantitative results and human visual quality compared to 17 methods. The proposed method achieves (1.9%, 1.8%, 4.2%, and 3.7%) gains in average PSNR and (4.2%, 2.9%, 6.7%, and 6.6%) gains in average SSIM over the sub-optimal method across the four datasets, respectively. We also demonstrate that our method can handle the challenging scenarios well. Source code is available at https://github.com/weimin581/demo_CSRNS.

Interpretable ADMM-CSNet for interrupted sampling repeater jamming suppression

Interrupted sampling repeater jamming (ISRJ) is a category of coherent jamming that greatly influences radars' detection performance. Since the ISRJ has greater power than true targets, ISRJ signals can be removed in the time domain. Due to frequency band loss, grating lobes will be produced if pulse compression (PC) is performed directly, which may generate false targets. Compressive sensing (CS) is an effective method to restore the original PC signal. However, it is challenging for classic CS approaches to manually select the optimization parameters (e.g., penalty parameters, step sizes, etc.) in different ISRJ backgrounds. In this article, a network method based on the Alternating Direction Method of Multipliers (ADMM), named ADMM-CSNet, is introduced to solve the problem. Based on the strong learning capacity of the deep network, all parameters in the ADMM are learned from radar data utilizing back-propagation rather than manually selecting in traditional CS techniques. Compared with classic CS approaches, a higher ISRJ removal signal restoration accuracy is reached faster. Simulation experiments indicate the proposal performs effectively and accurately for ISRJ removal signal reconstruction.

Transitive reasoning: A high-performance computing model for significant pattern discovery in cognitive IoT sensor network

Current research on the Internet of Things (IoT) has given rise to a new field of study called cognitive IoT (CIoT), which aims to incorporate cognition into the designs of IoT systems. Consequently, the CIoT inherits specific attributes and challenges from IoT. The CIoT applications generate vast, diverse, constantly changing, and time-dependent data due to the billions of devices involved. The efficient operation of these CIoT systems requires the extraction of valuable insights from vast data sources in a computationally efficient manner. Therefore, this study proposes transitive reasoning to glean significant concepts and patterns from a 21.25-year environmental dataset. To reduce the effects of missing entries, the proposed methodology includes a grouping of data using probabilistic clustering and applying total variance regularization in the alternate direction method of multipliers (ADMM) to regularize the sensory data. As a result, noisy entries will be less conspicuous. Afterward, it calculates the transitional plausibility value for each cluster using the transited value and then turns it into binary data to create concept lattices. In addition, each concept that is formed is assigned a weight, and the concept with the largest transitive strength value is chosen, followed by calculating the mean value. Therefore, this pattern is seen as significant. Experimental results on 21.25-year environmental data show an accuracy of over 99.5%, outperforming competing methods, as shown by cross-validation using multiple metrics.

Coordinated Optimal Operation Method for Snow-Shaped Distribution Networks Based on Game Theory

The snow-shaped distribution network is developed and upgraded from the traditional single-loop network and double-loop network structure. It is composed of three or four groups of single-loop networks in pairs that form a feeder cluster in the form of a ring network. Based on this topology, the coordinated optimization operation problem is studied. First, the game elements are analyzed, and then a cooperative game-based, coordinated optimization operation model is established by taking the minimum network loss and voltage deviation of the system as the utility function. Then, the alternating direction multiplier method (ADMM) is employed in Cplex solver to solve the established optimization model. Finally, a numerical case is given to verify the effectiveness of the proposed model and method. The results show that, by using the complementary difference relationship of source–charge characteristics between different regions in the snow-shaped distribution networks, the cooperative game model can realize the energy interconnection among different regions to improve the operation level.

Shaped pattern synthesis for hybrid analog–digital arrays via manifold optimization-enabled block coordinate descent

Hybrid analog–digital (HAD) architecture is a promising means to realize large-scale arrays owing to the judicious trade-off between system performance and hardware complexity. This paper investigates the beampattern shaping of HAD arrays through minimizing the beampattern matching error between desired and actual patterns. Due to the nonconvex constraints on analog and digital weights and the nonconvex nonsmooth objective function, the resultant codesign is NP-hard. To address this issue, we create an efficient algorithm by leveraging block coordinate descent (BCD) and Riemannian manifold optimization. We first equivalently represent the objective function as a smooth bi-quadratic function by introducing a uni-modulus auxiliary variable. Subsequently, we alternatingly optimize the scaling factor, digital weights, analog weights and auxiliary variable under the BCD framework, where the simultaneous update of analog weights and auxiliary variable is recast as uni-modular constrained quadratic programming which is efficiently solved by Riemannian Newton method, and the digital weights have a global optimal solution via Lagrangian multiplier method. We also derive an explicit convergence condition of this algorithm. Numerical results demonstrate that the proposed algorithm has superior performance and faster convergence speed than alternative algorithms, and produces nearly the same mainlobe gain as fully digital arrays with significantly fewer radio-frequency chains.

Dynamically regularized Lagrange multiplier schemes with energy dissipation for the incompressible Navier-Stokes equations

In this paper, we present efficient numerical schemes based on the Lagrange multiplier approach for the Navier-Stokes equations. By introducing a dynamic equation (involving the kinetic energy, the Lagrange multiplier, and a regularization parameter), we form a new system which incorporates the energy evolution process but is still equivalent to the original equations. Such nonlinear system is then discretized in time based on the backward differentiation formulas, resulting in a dynamically regularized Lagrange multiplier (DRLM) method. First- and second-order DRLM schemes are derived and shown to be unconditionally energy stable with respect to the original variables. The proposed schemes require only the solutions of two linear Stokes systems and a scalar quadratic equation at each time step. Moreover, with the introduction of the regularization parameter, the Lagrange multiplier can be uniquely determined from the quadratic equation, even with large time step sizes, without affecting accuracy and stability of the numerical solutions. Fully discrete energy stability is also proved with the Marker-and-Cell (MAC) discretization in space. Various numerical experiments in two and three dimensions verify the convergence and energy dissipation as well as demonstrate the accuracy and robustness of the proposed DRLM schemes.