DC Algorithm Research Articles

Research on Status Assessment and Operation and Maintenance of Electric Vehicle DC Charging Stations Based on XGboost

With the rapid development of electric vehicles, the infrastructure for charging stations is also expanding quickly, and the failure rate of charging piles is increasing. To address the effective operation and maintenance of charging stations, a method based on the XGBoost algorithm for electric vehicle DC charging stations is proposed. An operation and maintenance system is constructed based on state analysis, considering the operational status of the charging stations and users’ charging habits. Factors such as driving and charging habits, road traffic, and charging station equipment are taken into account. The training sample data are established using historical data, online monitoring data, and external environmental data, and the charging station status evaluation model is trained using the XGBoost algorithm. Based on the condition assessment results, a risk assessment model is established in combination with fault parameters. Risk tracking of the charging stations is conducted using the energy not charged (ENC), evaluating the risk level of each station and determining the operation and maintenance order. The optimal operation and maintenance model for DC charging stations, aimed at achieving both economic and reliability goals, is constructed to determine the operation and maintenance schedule for each station. The results of the case study demonstrate that the state evaluation and operation and maintenance strategy can significantly improve the reliability of the system and the overall benefits of operation and maintenance while meeting the required standards.

A boosted DC algorithm for non-differentiable DC components with non-monotone line search

A boosted DC algorithm for non-differentiable DC components with non-monotone line search

Online Stochastic DCA With Applications to Principal Component Analysis.

Stochastic algorithms are well-known for their performance in the era of big data. In this article, we study nonsmooth stochastic Difference-of-Convex functions (DC) programs-the major class of nonconvex stochastic optimization, which have a variety of applications in divers domains, in particular, machine learning. We propose new online stochastic algorithms based on the state-of-the-art DC Algorithm (DCA)-a powerful approach in nonconvex programming framework, in the online context of streaming data continuously generated by some (unknown) source distribution. The new schemes use the stochastic approximations (SAs) principle: deterministic quantities of the standard DCA are replaced by their noisy estimators constructed using newly arriving samples. The convergence analysis of the proposed algorithms is studied intensively with the help of tools from modern convex analysis and martingale theory. Finally, we study several aspects of the proposed algorithms on an important problem in machine learning: the expected problem in principal component analysis (PCA).

Large-scale robust regression with truncated loss via majorization-minimization algorithm

The utilization of regression methods employing truncated loss functions is widely praised for its robustness in handling outliers and representing the solution in the sparse form of the samples. However, due to the non-convexity of the truncated loss, the commonly used algorithms such as difference of convex algorithm (DCA) fail to maintain sparsity when dealing with non-convex loss functions, and adapting DCA for efficient optimization also incurs additional development costs. To address these challenges, we propose a novel approach called truncated loss regression via majorization-minimization algorithm (TLRM). TLRM employs a surrogate function to approximate the original truncated loss regression and offers several desirable properties: (i) Eliminating outliers before the training process and encapsulating general convex loss regression within its structure as iterative subproblems, (ii) Solving the convex loss problem iteratively thereby facilitating the use of a well-established toolbox for convex optimization. (iii) Converging to a truncated loss regression and providing a solution with sample sparsity. Extensive experiments demonstrate that TLRM achieves superior sparsity without sacrificing robustness, and it can be several tens of thousands of times faster than traditional DCA on large-scale problems. Moreover, TLRM is also applicable to datasets with millions of samples, making it a practical choice for real-world scenarios. The codebase for methods with truncated loss functions is accessible at https://i-do-lab.github.io/optimal-group.org/Resources/Code/TLRM.html.

Poisson image deblurring with frame-based nonconvex regularization

Poisson image deblurring, which aims to restore the latent image from its blurred and noisy observation, has drawn significant attention in image processing. Due to its ill-posed nature, enhancing image quality often involves incorporating a well-defined prior to effectively regularize the ill-posed inverse problem. Building upon the framelet system, we propose a frame-based nonconvex regularization method for Poisson image deblurring. The method is formulated by combining a data-fitting term with the difference of two norms, namely ℓ1 and ℓ2, on the latent image. We solve the optimization problem by combining the difference of convex functions algorithm (DCA) with the alternating direction method of multipliers (ADMM), establishing its convergence. We further employ a simulated annealing procedure and show that proposed algorithm almost certainly converges to a global minimum. Two different approaches are employed to handle the frame-based ℓ1 norm within the ADMM framework. In particular, the frame-based nonconvex regularization method is also considered for the blind Poisson problem. An effective recovery model and its algorithm are presented. Experimental results demonstrate the effectiveness of our proposed models compared with other models in terms of quantitative metrics and visual quality.

An inexact proximal linearized DC algorithm with provably terminating inner loop

Standard approaches to difference-of-convex (DC) programs require exact solution to a convex subproblem at each iteration, which generally requires noiseless computation and infinite iterations of an inner iterative algorithm. To tackle these difficulties, inexact DC algorithms have been proposed, mostly by relaxing the convex subproblem to an approximate monotone inclusion problem. However, there is no guarantee that such relaxation can lead to a finitely terminating inner loop. In this paper, we point out the termination issue of existing inexact DC algorithms by presenting concrete counterexamples. Exploiting the notion of ϵ-subdifferential, we propose a novel inexact proximal linearized DC algorithm termed tPLDCA. Despite permission to a great extent of inexactness in computation, tPLDCA enjoys the same convergence guarantees as exact DC algorithms. Most noticeably, the inner loop of tPLDCA is guaranteed to terminate in finite iterations as long as the inner iterative algorithm converges to a solution of the proximal point subproblem, which makes an essential difference from prior arts. In addition, by assuming the first convex component of the DC function to be pointwise maximum of finitely many convex smooth functions, we propose a computational friendly surrogate of ϵ-subdifferential, whereby we develop a feasible implementation of tPLDCA. Numerical results demonstrate the effectiveness of the proposed implementation of tPLDCA.

Random distribution and adsorption characteristics of metal particles and visualization algorithm for DC GIS/GIL

Random distribution and adsorption characteristics of metal particles and visualization algorithm for DC GIS/GIL

Non-monotone Boosted DC and Caputo Fractional Tailored Finite Point Algorithm for Rician Denoising and Deblurring

Non-monotone Boosted DC and Caputo Fractional Tailored Finite Point Algorithm for Rician Denoising and Deblurring

Markov chain stochastic DCA and applications in deep learning with PDEs regularization

This paper addresses a large class of nonsmooth nonconvex stochastic DC (difference-of-convex functions) programs where endogenous uncertainty is involved and i.i.d. (independent and identically distributed) samples are not available. Instead, we assume that it is only possible to access Markov chains whose sequences of distributions converge to the target distributions. This setting is legitimate as Markovian noise arises in many contexts including Bayesian inference, reinforcement learning, and stochastic optimization in high-dimensional or combinatorial spaces. We then design a stochastic algorithm named Markov chain stochastic DCA (MCSDCA) based on DCA (DC algorithm) - a well-known method for nonconvex optimization. We establish the convergence analysis in both asymptotic and nonasymptotic senses. The MCSDCA is then applied to deep learning via PDEs (partial differential equations) regularization, where two realizations of MCSDCA are constructed, namely MCSDCA-odLD and MCSDCA-udLD, based on overdamped and underdamped Langevin dynamics, respectively. Numerical experiments on time series prediction and image classification problems with a variety of neural network topologies show the merits of the proposed methods.

Learning graph Laplacian with MCP

We consider the problem of learning a graph under the Laplacian constraint with a non-convex penalty: minimax concave penalty (MCP). For solving the MCP penalized graphical model, we design an inexact proximal difference-of-convex algorithm (DCA) and prove its convergence to critical points. We note that each subproblem of the proximal DCA enjoys the nice property that the objective function in its dual problem is continuously differentiable with a semismooth gradient. Therefore, we apply an efficient semismooth Newton method to subproblems of the proximal DCA. Numerical experiments on various synthetic and real data sets demonstrate the effectiveness of the non-convex penalty MCP in promoting sparsity. Compared with the existing state-of-the-art method, our method is demonstrated to be more efficient and reliable for learning graph Laplacian with MCP.

An Accelerated Double-Proximal Gradient Algorithm for DC Programming

The double-proximal gradient algorithm (DPGA) is a new variant of the classical difference-of-convex algorithm (DCA) for solving difference-of-convex (DC) optimization problems. In this paper, we propose an accelerated version of the double-proximal gradient algorithm for DC programming, in which the objective function consists of three convex modules (only one module is smooth). We establish convergence of the sequence generated by our algorithm if the objective function satisfies the Kurdyka–[Formula: see text]ojasiewicz (K[Formula: see text]) property and show that its convergence rate is not weaker than DPGA. Compared with DPGA, the numerical experiments on an image processing model show that the number of iterations of ADPGA is reduced by 43.57% and the running time is reduced by 43.47% on average.

DC algorithms in Hilbert spaces and the solution of indefinite infinite-dimensional quadratic programs

DC algorithms in Hilbert spaces and the solution of indefinite infinite-dimensional quadratic programs

Vertex Prime Degree-Based Nonisomorphic Topology Automatic Search Algorithm for DC–DC Converters With Two Switches

The development of DC-DC converter topologies has been a topic of great interest due to their increasing use in various industrial applications. However, most of the topology-building methods are artificial, which may result in the miss of potentially useful topologies and incur a heavy time cost due to the limitations of human experience. To address the above issue, this paper proposes an automatic search algorithm for finding useful DC-DC converter topologies with two switches, which have broad application prospects in renewable energy generation and DC microgrids. The proposed algorithm is based on the vertex prime degree (VPD) of the converters, which automatically searches out all available DC-DC converter topologies and avoids generating vast useless isomorphic topologies. As an example, for the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> type DC-DC converters, which have two switches, one diode, one capacitor, and one inductor, this paper founds 40 available <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> type DC-DC converter topologies using the proposed algorithm, including 36 new topologies and 4 existing topologies in the literature. The proposed search algorithm's effectiveness is verified by circuit simulation and experiment. Furthermore, the topology search time is compared among the proposed algorithm, the programmable topology search method using vertex degree classification and the topology search algorithm using permutation and combination. Finally, it is demonstrated that the new algorithm can search out all the available <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> type DC-DC converters in just 11 seconds, while the existing four topologies were proposed in 2007 and 2020, respectively, which took more than ten years. This paper provides a fast and ergodic way for finding DC-DC converter topologies with two switches.

A bundle-type method for nonsmooth DC programs

A bundle method for minimizing the difference of convex (DC) and possibly nonsmooth functions is developed. The method may be viewed as an inexact version of the DC algorithm, where each subproblem is solved only approximately by a bundle method. We always terminate the bundle method after the first serious step. This yields a descent direction for the original objective function, and it is shown that a stepsize of at least one is accepted in this way. Using a line search, even larger stepsizes are possible. The overall method is shown to be globally convergent to critical points of DC programs. The new algorithm is tested and compared to some other solution methods on several examples and realistic applications.

Difference-of-Convex Algorithm with Extrapolation for Nonconvex, Nonsmooth Optimization Problems

In this paper, we focus on the problem of minimizing the sum of a nonconvex differentiable function and a difference of convex (DC) function, where the differentiable function is not restricted to the global Lipschitz gradient continuity assumption. This problem covers a broad range of applications in machine learning and statistics, such as compressed sensing, signal recovery, sparse dictionary learning, matrix factorization, etc. We first take inspiration from the Nesterov acceleration technique and the DC algorithm to develop a novel algorithm for the considered problem. We then study the subsequential convergence of our algorithm to a critical point. Furthermore, we justify the global convergence of the whole sequence generated by our algorithm to a critical point and establish its convergence rate under the Kurdyka–Łojasiewicz condition. Numerical experiments on the nonnegative matrix completion problem are performed to demonstrate the efficiency of our algorithm and its superiority over well-known methods.

A new device-free localization method for RSS data with considering correlations

Device-free localization (DFL) is an emerging intelligent sensing technique with challenging issues due to the highly correlated data. Localization performance has been demonstrated from algorithmic as well as modelling perspectives, for example, by including various sparsity constraints. The general sparse regularization method simultaneously estimates parameters and selects features, but its performance relies heavily on the correlations among features, which leads to generalization errors. Our goal in this study is to formulate a DFL method based on independently interpretable sparse coding to improve the accuracy and efficiency of localization. The scheme uses a novel correlation constraint of sensing matrix columns to handle the high correlation of the received signal strength (RSS) data, overcoming not only the fluctuation of RSS due to environmental changes but also avoiding overfitting through identification of informative variables that provide interpretable results. Meanwhile, the minimax concave penalty (MCP) is proposed as a sparse regularizer to obtain strong sparsity and an exact estimate. We propose using the difference of convex functions algorithm (DCA) and non-convex proximal splitting to address the non-convexity problem. Extensive experiments were performed in a cluttered indoor laboratory and open outdoor environment to verify the efficacy of the proposed method.

Fused robust geometric nonparallel hyperplane support vector machine for pattern classification

Recently, introducing nonconvex loss functions in support vector machine (SVM) to improve the robustness against varies noises has been drawing much attention. In this paper, we first construct a new robust capped asymmetric elastic net (CaEN) loss function. Second, we describe a novel robust Huberized kernel-based (HK) loss function and theoretically demonstrate several important properties, such as smoothness, boundness and the trade-off between the standard least squares and the truncated least squares. Finally, we apply the CaEN loss and the HK loss into elastic net nonparallel hyperplane SVM (ENNHSVM) to develop a fused robust geometric nonparallel SVM (FRGNHSVM). The proposed FRGNHSVM not only inherits the advantages of ENNHSVM but also improves the robustness of classification problems. An efficient Pegasos-based DC (difference of convex functions) algorithm is implemented to solve the FRGNHSVM optimization problem. In comparison with four famous SVMs, including Lagrangian SVM, twin SVM, pinball SVM and C-loss twin SVM, experimental results on simulations and twelve UCI datasets show that the proposed FRGNHSVM can often improve more than 5% average prediction accuracy. Moreover, the performance of the high prediction accuracy of FRGHNSVM is more significant along with the ratio of label noise increasing, indicating its superiority in dealing with label-contaminated datasets.

Infrared Dim Small Target Detection Based on Nonconvex Constraint with L1–L2 Norm and Total Variation

Infrared dim small target detection has received a lot of attention, because it is a crucial component of the IR search and track systems (IRST). The robust principal component analysis (RPCA) is a common detection framework, which works with poor performance with complex background edges and sparse clutters due to the inappropriate approximation of sparse items. A nonconvex constraint detection method based on the difference between the L1 and L2 (L1–L2) norm and total variation (TV) is presented. The L1–L2 norm is a more accurate sparse item approximation of L0 norm, which can achieve a better description of the sparse item to separate the target from the complex backgrounds. Then, the total variation norm is conducted on the target image to suppress the sparse clutters. The new model is solved using the alternating direction method of multipliers (ADMM) method. Then, the subproblems in the model are tackled by the difference of convex algorithm (DCA) and the Newton conjugate gradient (Newton-CG) solving L1–L2 norm and TV norm, respectively. In the experiment, we conducted experiments on multiple and single target datasets, and the proposed model outperforms the state-of-the-art (SOTA) methods in terms of background suppression and robustness to accurately detect the target. It can achieve a higher true position rate (TPR) with a low false position rate (FPR).

Nearest-neighbor field algorithm based on patchMatch for myocardial perfusion motion estimation/correction

Deformation correction and recovery of dynamic magnetic resonance images (DMRI) with low complexity algorithms without compromising image quality is a challenging problem. We proposed a motion estimation deformation-correction compressive sensing (DC-CS) scheme to recover dynamic images from its undersampled measurements. We simplify the complex optimization problem into three sub-problems. The contributions of this research are: introducing a global search strategy instead of the DC registration step, guaranteeing a non-explicit motion estimation that avoids any spatial alignment or registration of the images, and lowering the computational cost to the minimum by using PatchMatch (PM). The simulation result shows that the PM algorithm accelerates the recovery time without losing the quality in comparison with the DC algorithm.

On the Rate of Convergence of the Difference-of-Convex Algorithm (DCA)

In this paper, we study the non-asymptotic convergence rate of the DCA (difference-of-convex algorithm), also known as the convex–concave procedure, with two different termination criteria that are suitable for smooth and non-smooth decompositions, respectively. The DCA is a popular algorithm for difference-of-convex (DC) problems and known to converge to a stationary point of the objective under some assumptions. We derive a worst-case convergence rate of O(1/N)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(1/\\sqrt{N})$$\\end{document} after N iterations of the objective gradient norm for certain classes of DC problems, without assuming strong convexity in the DC decomposition and give an example which shows the convergence rate is exact. We also provide a new convergence rate of O(1/N) for the DCA with the second termination criterion. Moreover, we derive a new linear convergence rate result for the DCA under the assumption of the Polyak–Łojasiewicz inequality. The novel aspect of our analysis is that it employs semidefinite programming performance estimation.