Insulator detection is an important task for safe and reliable operation of smart grid. Due to various background interferences in insulator images, most traditional image processing methods cannot achieve good performance. In this paper, a new method based on Log AdaBoost is proposed for insulator detection. Firstly, our boosting algorithm optimizes Polylog loss function rather than Exponential function in classical AdaBoost. We use gradient descent to optimize our loss function while the coordinate descent method is used in classical AdaBoost. Secondly, a new weight updating strategy is taken to find the weak classifier relevant to the label under the current weight distribution. In other word, the weight is updated towards the negative gradient of loss function to find the optimal weak classifier. Thirdly, a neighborhood feature is proposed in this paper, and this Haar-like feature can make the pixel difference between the insulator and the background obvious. Experimental results on two databases (UCI and ACDC) show that the proposed algorithm achieves the lowest test error on 11 of the 20 UCI datasets (second-lowest on the other nine), and on ACDC it yields lower testing error with the fewest weak classifiers and the smallest margin variance across the four labels, indicating better generalization than other AdaBoost variants. Finally, on the CPLID insulator detection dataset, the proposed method achieves an AUC of 0.82 with only 21k parameters.

ABSTRACT This paper proposed a new multistage hybrid algorithm MH‐IK to solve the inverse kinematics (IK) problem of redundant manipulators in terms of position, orientation, and collision errors. An improved cyclic coordinate descent method is proposed to satisfy the iteration of prismatic joints and avoid singularities. Halley's method is integrated to achieve fast convergence. On the basis of geometric analysis and the Beta distribution, a global search method is developed to overcome the local minimum problem. Four strategies are designed to further improve the adaptability during iterative loops. The proposed algorithm is applied to a seven‐degrees‐of‐freedom mill relining manipulator. Unlike conventional arms, the IK solution of this special manipulator has more requirements to be satisfied, including solvability, stability, real‐time, joint limits, and collision avoidance in a confined inner workspace. The superiority of MH‐IK is demonstrated through convergence analysis, ablation and comparison experiments against nine nonlinear algorithms and three millisecond‐level solvers. Furthermore, the hardware experiments are carried out in an established digital twin system to further verify the effectiveness of the proposed method. Although MH‐IK lacks solution diversity, it significantly outperforms other algorithms in almost all metrics, such as 5.27 ms solving time, 99.5% success rate, and 0.51% collision rate.

Inspired by Polyak’s heavy-ball method, this paper proposes an adaptive deterministic block coordinate descent method with momentum (mADBCD) for efficiently solving large-scale linear least-squares problems. The proposed method introduces a novel column selection criterion based on the Euclidean norm of the residual vector of the normal equation. In contrast to classical block coordinate descent methods, mADBCD does not require a fixed pre-partitioning of the column indices of the coefficient matrix and avoids the expensive computation of Moore Penrose pseudoinverses of submatrices at each iteration. The method adaptively updates the block index set at each step, thereby improving both flexibility and scalability. When the coefficient matrix is of full column rank, we prove that mADBCD converges linearly to the unique solution of the least-squares problem. Numerical experiments are conducted to show that mADBCD outperforms several recent block coordinate descent methods in terms of iteration count and CPU time. In particular, when solving extremely sparse least-squares problems, mADBCD is the first block coordinate descent method reported to achieve CPU time nearly comparable to that of the classical least squares QR (LSQR) method [Paige and Saunders, ACM Trans. Math. Softw., 8 (1982)].

An efficient greedy quasi block coordinate descent method for solving linear least-squares problems

This paper presents a novel framework for the analysis and design of randomized algorithms for solving linear systems, including consistent or inconsistent, full rank or rank-deficient. The framework is formulated with four randomized sampling parameters, which allows for the unification of existing randomization algorithms, such as the doubly stochastic Gauss-Seidel (DSGS) method, randomized Kaczmarz (RK) method, and randomized coordinate descent (RCD) method. Compared with the projection-based block algorithms where a pseudoinverse for solving a least-squares problem is utilized at each iteration, our design is pseudoinverse-free. Furthermore, the flexibility of the new approach also enables the design of a number of new methods as special cases. Polyak's heavy ball momentum technique is also incorporated into the framework to improve the convergence behaviour of the method. An alternative convergence analysis of momentum variants of randomized iterative methods is proposed, where smaller convergence factors for RK and RCD with momentum are obtained. Additionally, an accelerated linear rate for the case of the norm of expected iterates is proven. Finally, numerical experiments are provided to confirm our results.

The sharp increase in Internet of Things (IoT) terminal numbers imposes significant pressure on energy and wireless spectrum resources. Battery-free IoT technology has become an effective solution to address the high power consumption and cost issues of traditional IoT systems. While leveraging backscatter communication, battery-free IoT faces challenges such as low throughput and poor fairness among wireless links. To tackle these problems, this study proposes a low-power hybrid communication mechanism for terminals. Within this mechanism, a time-frame partitioning method for hybrid communication strategies is designed based on sensing results of licensed spectrum channels. Considering terminal power constraints, quality of service (QoS) requirements of primary communication links, and time resource limitations, a hybrid communication strategy model is established to jointly optimize fairness and maximize throughput. To resolve the non-convexity in the Multi-objective Lexicographical Optimization Problem (MLOP), the Block Coordinate Descent (BCD) method and auxiliary variables are introduced. Simulation results demonstrate that, compared to the baseline scheme, the proposed approach reduces the throughput gap between links from 85.4% to 0.32% when the channel gain differences are small, while the total system throughput decreases by only 8.81%. As the channel gain disparity increases, the baseline scheme exhibits a more pronounced disadvantage in terms of throughput fairness, while the proposed approach still reduces the throughput gap between the best and worst links from 91.02% to 0.684% at the cost of a 9.18% decrease in total system throughput. These results demonstrate that the proposed scheme effectively balances fairness and throughput performance across diverse channel conditions, ensuring relatively equitable quality of service for all users in the IoT network.

Joint clustering and feature selection based on trace ratio model and coordinate descent method

Graph-based multiview clustering methods have gained significant attention in recent years. In particular, incorporating graph filtering into these methods allows for the exploration and utilization of both feature and topological information, resulting in a commendable improvement in clustering accuracy. However, these methods still exhibit several limitations: 1) the graph filters are predetermined, which disconnects the link with subsequent clustering tasks and 2) the separability of the filtered features is poor, which may not be suitable for the clustering. To mitigate these aforementioned issues, we propose Multiview Clustering via Block Diagonal Graph Filtering (MvC-BDGF), which can learn cluster-friendly graph filters. Specifically, the block diagonal graph filter with localized characteristics, which could make the filtered features very discriminating, is innovatively designed. The MvC-BDGF model seamlessly integrates the learning of graph filters with the acquisition of consensus graphs, forming a unified framework. This integration allows the model to obtain optimal filters and simultaneously acquire corresponding clustering labels. To solve the optimization problem in the MvC-BDGF model, an iterative solver based on the coordinate descent method is devised. Finally, a large number of experiments on benchmark datasets fully demonstrate the effectiveness and superiority of the proposed model. The code is available at https://github.com/haonanxin/MvC-BDGF_code.

Due to the excellent performance of spectral clustering (SC), it has been widely used in many fields of application. However, the high computational complexity and two successive steps have limited SC's development. In addition, the traditional SC is formulated to maximize the arithmetic mean of trace ratios which is dominated by the larger objectives and may reduce the recognition accuracy in practical applications. In this article, we propose a novel graph cut criterion to minimize the trace ratios of harmonic mean with objectives, which can avoid the worst-cluster issue without imposing any regularization or constraints. Furthermore, an efficient and effective coordinate descent (CD) method is exploited to achieve a one-step solution. Therefore, this article can simultaneously solve three main challenges in a unified framework. Extensive experiments verify that the harmonic fast one-step graph cut (HFOC) achieves superior clustering performance with relatively less time-consuming compared to the other state-of-the-art clustering methods.

Using examples of photonic crystal interference optical elements such as bends of waveguide structures, an intersection of three waveguides, a radiation input node, a Y-shaped logical gate NOT, and a logical gate NOT on a crystal with self-collimation, we discuss two approaches to the synthesis of integrated optics elements: non-stochastic methods of gradient-free optimization (zero-order optimization methods) and a genetic algorithm. Both approaches involve solving the direct diffraction problem using the FDTD method. We conclude that these approaches are suited for designing photonic crystal optical elements: a comparison of the calculated results in terms of the efficiency criterion demonstrates an advantage of the author's modified genetic algorithm over the coordinate descent and Hooke-Jeeves methods for elements in which radiation does not propagate along a straight path. Meanwhile for elements that conduct radiation along a straight waveguide, zero-order optimization methods provide the same efficiency as genetic optimization (more than 99%), while the computational complexity of these methods is lower. Particular attention is paid to the analysis of the “partial enumeration” method. Using the example of a photonic crystal waveguide with a 120°-bending, it is shown that the element designed using this method is characterized by virtually lossless radiation transmission, while its computational complexity is 2 times lower than that of the genetic algorithm.

Mobile edge computing (MEC) and wireless power transmission (WPT) can provide energy supply and task computing for wireless devices, effectively improving the energy efficiency of devices. On the basis of wireless energy transfer for drones, we provide an approach to optimizing energy usage for edge computing systems. By simultaneously optimizing the energy harvesting (EH) duration, user transmission power, as well as offloading choice, the presented method reduces the overall energy usage of the system. We decompose the optimization problem into two sub-problems with the block coordinate descent method (BCD). Simulation results suggest that our presented system energy consumption optimization method outperforms other baseline schemes and the energy required by the system can be significantly reduced.

The article is devoted to solving the problems of automation of the pasteurizer in LLC «Baltika Brewing Company» - «Voronezh Brewery» to improve the quality of control. The control system structure was developed based on the SIEMENS S7-400 controller, input/output modules SM321, SM331, SM322, SM332 and IEI PPC-5190A touch panel. The equipment includes local automation tools: SENSYCON PT100 temperature sensors; Endress+Hauser Cerabar S PMC631, Aplysens 0…10 bar pressure sensors; Endress+Hauser electromagnetic flow meters; HAFFMANS-PENTAIR oxygen meter; Enress+Hauser CLD134-PLC148AB2 conductivity meter; SPIRAX SARCO valves. The DANFOSS 131B2132 FC-302 frequency converter was adjusted to control the pump to enable working with small beer flows. Algorithmic and software support for the SIEMENS S7-400 control controller (Step7 environment) and the IEI PPC-5190A touch panel (WinCC environment) has been developed. To control the pasteurization process, it is proposed to implement a scheme for combined beer temperature control (steam flow rate) with disturbance compensation based on the heating steam pressure in the pipeline. To synthesize the algorithm for digital combined control, discrete dynamic models of the control channel (“heating steam flow rate – beer temperature at the pasteurization section outlet”) and the disturbance channel (“steam pressure in the coolant supply pipeline – beer temperature at the pasteurization section outlet”) were identified. The channel models were identified based on the experimental data obtained on the pasteurizer using the least squares method (LSM). A numerical optimization method (coordinate descent method) was used to calculate the settings of the digital PID controller and compensator for the control and disturbance channels. Model experiments were conducted, which showed that the use of this algorithm significantly reduces the fluctuation of beer temperature during pasteurization. To synthesize the algorithm, the author's programs for identifying discrete dynamic models of object channels and optimizing the settings of digital regulators and compensators were used. The process control system was put into operation.

Aiming at the issue of how to improve the system transmission rate in a multiple Internet of things (IoT) device application scenario, we propose the resource allocation algorithm of the symbiotic radio communication system under multiple backscatter devices (BDs) assisted by unmanned aerial vehicle (UAV). We formulate the optimization problem of maximizing BDs’ sum rate by jointly optimizing the time allocation, BDs’ reflection coefficient and UAV location under constraints of BD’s harvested energy, quality of service (QoS) of cellular user and UAV. Since the problem is non-convex, it is difficult to solve directly. Therefore, the iterative algorithm based on block coordinate descent (BCD) method can be adopted, which decomposes the optimization problem into three sub-problems: time allocation, reflection coefficients of BDs and UAV location. For non-convex sub-problems, we utilize the successive convex approximation (SCA) technique to transform it into convex optimization problems, and we prove that the conversion is convex optimization problems. Simulation results show that our proposed algorithm converges fast, and significantly improves the system transmission rate compared with other schemes.

This work proposes a power-efficient framework for adaptive video streaming in UAV-assisted wireless networks specially designed for disaster-hit areas where existing base stations are nonfunctional. Delivering high-quality videos requires higher video rates and more resources, which leads to increased power consumption. With the increasing demand of mobile video, efficient bandwidth allocation becomes essential. In shared networks, users with lower bitrates experience poor video quality when high-bitrate users occupy most of the bandwidth, leading to a degraded and unfair user experience. Additionally, frequent video rate switching can significantly impact user experience, making the video rates’ smooth transition essential. The aim of this research is to maximize the overall users’ quality of experience in terms of power-efficient adaptive video streaming by fair distribution and smooth transition of video rates. The joint optimization includes power minimization, efficient resource allocation, i.e., transmit power and bandwidth, and efficient two-dimensional positioning of the UAV while meeting system constraints. The formulated problem is non-convex and difficult to solve with conventional methods. Therefore, to avoid the curse of complexity, the block coordinate descent method, successive convex approximation technique, and efficient iterative algorithm are applied. Extensive simulations are performed to verify the effectiveness of the proposed solution method. The simulation results reveal that the proposed method outperforms 95–97% over equal allocation, 77–89% over random allocation, and 17–40% over joint allocation schemes.

An adaptive accelerated coordinate descent method with non-uniform sampling

A monotone block coordinate descent method for solving absolute value equations

Dictionary learning is an effective tool for pattern recognition and classification of time series data. However, real-world time series data often exhibit temporal misalignment due to temporal delay, scaling or other temporal transformations, which poses significant challenges for effective dictionary learning. Dynamic time warping (DTW) is commonly used for dealing with such misalignment issues. Nevertheless, the DTW suffers overfitting or information loss due to its discrete nature in aligning time series data. To address this issue, we propose a generalized time warping invariant dictionary learning algorithm in this paper. Our approach features a generalized time warping operator, which consists of linear combinations of continuous basis functions for facilitating continuous temporal warping. The integration of the proposed operator and the dictionary learning is formulated as an optimization problem, where the block coordinate descent method is employed to jointly optimize warping paths, dictionaries, and sparse coefficients. The optimized results are then used as hyperspace distance measures to feed classification and clustering algorithms. The superiority of the proposed method in terms of dictionary learning, classification, and clustering is validated through ten sets of public datasets in comparison with various benchmark methods.

On the greedy coordinate descent methods for solving large linear least-squares problems

The proliferation of mobile terminal applications and the increasing energy consumption of chips have raised concerns about insufficient power in mobile user terminals. In response to this issue, this paper proposes a joint optimization algorithm for UAV-assisted caching and charging based on non-orthogonal multiple access (NOMA) within the context of mobile edge caching scenarios. The proposed algorithm considers the revenue generated from UAVs providing caching and charging services to users, as well as the cost associated with leasing cache files and the UAV energy consumption. The optimization problem aimed at maximizing UAV utility is established under constraints related to power and cache capacity. To address this mixed-integer programming problem, we divided it into two parts. The first part uses the Stackelberg–Bertrand game to optimize file pricing and the UAV cache strategy. In the second part, the block coordinate descent (BCD) method is used to optimize the UAV transmission power distribution, positioning, and user pairing. The joint optimization problem is divided into three subproblems, which use the Lagrange multiplier method, a simulated annealing algorithm, and a particle swarm optimization algorithm. Simulation results demonstrate that the proposed algorithm effectively reduces user transmission delay while also improving overall revenue generated by UAVs.

ABSTRACTFor solving symmetric eigenvalue problems of extremely large matrices that cannot be stored in a whole in the computer memory, we propose a class of admissibly randomized coordinate descent methods by minimizing the corresponding Rayleigh quotients. These iteration methods only call of and operate on a column of the matrix at each of their iteration steps, so they require a small computer memory and have a small computational complexity. We analyze the convergence property of these admissibly randomized coordinate descent methods and confirm their implemental effectiveness by numerical experiments.