Search Results (150)

This paper proposes a new proximal iteratively reweighted nuclear norm method for a class of nonconvex and nonsmooth optimization problems. The primary contribution of this work is the incorporation of line search technique based on dimensionality reduction and extrapolation. This strategy overcomes parameter constraints by enabling adaptive dynamic adjustment of the extrapolation/proximal parameters (α_k, β_k, μ_k). Under the Kurdyka–Łojasiewicz framework for nonconvex and nonsmooth optimization, we prove the global convergence and linear convergence rate of the proposed algorithm. Additionally, through numerical experiments using synthetic and real data in matrix completion problems, we validate the superior performance of the proposed method over well-known methods. Full article

We study the generalization properties of stochastic optimization methods under adaptive data sampling schemes, focusing on the setting of pairwise learning, which is central to tasks like ranking, metric learning, and AUC maximization. Unlike pointwise learning, pairwise methods must address statistical dependencies between input pairs—a challenge that existing analyses do not adequately handle when sampling is adaptive. In this work, we extend a general framework that integrates two algorithm-dependent approaches—algorithmic stability and PAC–Bayes analysis for this purpose. Specifically, we examine (1) Pairwise Stochastic Gradient Descent (Pairwise SGD), widely used across machine learning applications, and (2) Pairwise Stochastic Gradient Descent Ascent (Pairwise SGDA), common in adversarial training. Our analysis avoids artificial randomization and leverages the inherent stochasticity of gradient updates instead. Our results yield generalization guarantees of order $n^{-1/2}$ under non-uniform adaptive sampling strategies, covering both smooth and non-smooth convex settings. We believe these findings address a significant gap in the theory of pairwise learning with adaptive sampling. Full article

In this paper, we propose a sparse distributionally robust optimization (DRO) model incorporating the Conditional Value-at-Risk (CVaR) measure to control tail risks in uncertain environments. The model utilizes sparsity to reduce transaction costs and enhance operational efficiency. We reformulate the problem as a Min-Max-Min optimization and convert it into an equivalent non-smooth minimization problem. To address this computational challenge, we develop an approximate discretization (AD) scheme for the underlying continuous random vector and prove its convergence to the original non-smooth formulation under mild conditions. The resulting problem can be efficiently solved using a subgradient method. While our analysis focuses on CVaR penalty, this approach is applicable to a broader class of non-smooth convex regularizers. The experimental results on the portfolio selection problem confirm the effectiveness and scalability of the proposed AD algorithm. Full article

The quadratic regularization technique is widely used in the literature for constructing efficient algorithms, particularly for solving nonsmooth optimization problems. We propose an inexact nonsmooth quadratic regularization algorithm for solving large-scale optimization, which involves a large-scale smooth separable item and a nonsmooth one. The main difference between our algorithm and the (exact) quadratic regularization algorithm is that it employs inexact gradients instead of the full gradients of the smooth item. Also, a slightly different update rule for the regularization parameters is adopted for easier implementation. Under certain assumptions, it is proved that the algorithm achieves a first-order approximate critical point of the problem, and the iteration complexity of the algorithm is $O\left({\epsilon }^{-2}\right)$. In the end, we apply the algorithm to solve LASSO problems. The numerical results show that the inexact algorithm is more efficient than the corresponding exact one in large-scale cases. Full article

This research is concerned with design optimization of control systems. Our case study deals with magnetic levitation, in which an essential part is a solenoid. Its dimensions, along with controller parameters, form the optimization variables. We present a novel way of writing the explicit expression of the solenoid’s force acting on a magnetic dipole, as well as its first derivatives. Numerical tests using non-gradient search algorithms show the difference in optimal designs provided by these methods. Since such optimization depends on output signals, a comparison of step response analysis methods is presented. Full article

In modern vehicles, Autonomous Driving Systems (ADSs) are designed to operate partially or fully without human intervention. The ADS pipeline comprises multiple layers, including sensors, perception, localization, mapping, path planning, and control. The Robot Operating System (ROS) is a widely adopted framework that supports the modular development and integration of these layers. Among them, the path-planning and control layers remain particularly challenging due to several limitations. Classical path planners often struggle with non-smooth trajectories and high computational demands. Meta-heuristic optimization algorithms have demonstrated strong theoretical potential in path planning; however, they are rarely implemented in real-time ROS-based systems due to integration challenges. Similarly, traditional PID controllers require manual tuning and are unable to adapt to system disturbances. This paper proposes a ROS-based ADS architecture composed of eight integrated nodes, designed to address these limitations. The path-planning node leverages a meta-heuristic optimization framework with a cost function that evaluates path feasibility using occupancy grids from the Hector SLAM and obstacle clusters detected through the DBSCAN algorithm. A dynamic goal-allocation strategy is introduced based on the LiDAR range and spatial boundaries to enhance planning flexibility. In the control layer, a modified Pure Pursuit algorithm is employed to translate target positions into velocity commands based on the drift angle. Additionally, an adaptive PID controller is tuned in real time using the Differential Evolution (DE) algorithm, ensuring robust speed regulation in the presence of external disturbances. The proposed system is practically validated on a four-wheel differential drive robot across six scenarios. Experimental results demonstrate that the proposed planner significantly outperforms state-of-the-art methods, ranking first in the Friedman test with a significance level less than 0.05, confirming the effectiveness of the proposed architecture. Full article

In this work, we consider the problem of minimizing a quasi-convex function over a nonempty closed convex constrained set. In order to approximate a solution of the considered problem, we propose delayed star subgradient methods. The main feature of the proposed methods is that it allows us to use the stale star subgradients when updating the next iteration rather than computing the new star subgradient in every iteration. We subsequently investigate the convergence results of sequences generated by the proposed methods. Finally, we present some numerical experiments on the Cobb–Douglas production efficiency problem to illustrate the effectiveness of the proposed method. Full article

Since its publication in the 1960s, the Kalman Filter (KF) has been a powerful tool in optimal state estimation. However, the KF and most of its variants have mainly focused on the state estimation of smooth systems. In this work, we propose a new algorithm called the Discrete Unilateral Constrained Extended Kalman Filter (DUCEKF) that expands the capabilities of the Extended Kalman Filter (EKF) to a class of hybrid mechanical systems known as systems with unilateral constraints. Such systems are non-smooth in position and discontinuous in velocity. Lyapunov stability theory is invoked to establish sufficient conditions for the estimation error stability of the proposed algorithm. A comparison of the proposed algorithm with the EKF is conducted in simulation through a case study to demonstrate the superiority of the DUCEKF for the state estimation tasks in this class of systems. Simulations and an experiment were developed in this case study to validate the performance of the proposed algorithm. The experiment was conducted using electronic hardware that consists of an Embedded System (ES) called “Mikromedia for dsPIC33EP” and an external DAC-12 Click board, which includes a Digital-to-Analog Converter (DAC) from Texas Instruments. Full article

This paper proposes a Distributed Adaptive Regularization Algorithm (DARN) for solving composite non-convex and non-smooth optimization problems in multi-agent systems. The algorithm employs a three-phase iterative framework to achieve efficient collaborative optimization: (1) a local regularized optimization step, which utilizes proximal mappings to enforce strong convexity of weakly convex objectives and ensure subproblem well-posedness; (2) a consensus update based on doubly stochastic matrices, guaranteeing asymptotic convergence of agent states to a global consensus point; and (3) an innovative adaptive regularization mechanism that dynamically adjusts regularization strength using local function value variations to balance stability and convergence speed. Theoretical analysis demonstrates that the algorithm maintains strict monotonic descent under non-convex and non-smooth conditions by constructing a mixed time-scale Lyapunov function, achieving a sublinear convergence rate. Notably, we prove that the projection-based update rule for regularization parameters preserves lower-bound constraints, while spectral decay properties of consensus errors and perturbations from local updates are globally governed by the Lyapunov function. Numerical experiments validate the algorithm’s superiority in sparse principal component analysis and robust matrix completion tasks, showing a 6.6% improvement in convergence speed and a 51.7% reduction in consensus error compared to fixed-regularization methods. This work provides theoretical guarantees and an efficient framework for distributed non-convex optimization in heterogeneous networks. Full article

Wide-range electric submersible centrifugal pumps (ESPs) are critical for offshore oilfields but suffer from narrow high-efficiency ranges and frictional losses under dynamic reservoir conditions. This study introduces bio-inspired dimple-type non-smooth surfaces on impeller blades to enhance hydraulic performance. A combined numerical-experimental approach was employed: a 3D CFD model with the k-ω turbulence model analyzed oil–water flow (1:9 ratio) to identify optimal dimple placement, while parametric studies tested diameters (0.6–1.2 mm). Experimental validation used 3D-printed prototypes. Results revealed that dimples on the pressure surface trailing edge reduced boundary layer separation, achieving a 12.98% head gain and 8.55% efficiency improvement at 150 m³/d in simulations, with experimental tests showing an 11.5% head increase and 4.6% efficiency gain at 130 m³/d. The optimal dimple diameter (0.9 mm, 2% of blade chord) balanced performance and manufacturability, demonstrating that bio-inspired surfaces improve ESP efficiency. This work provides practical guidelines for deploying drag reduction technologies in petroleum engineering, with a future focus on wear resistance in abrasive flows. Full article

As an emerging energy-saving approach, bio-inspired drag reduction technology has become a key research direction for reducing energy consumption and greenhouse gas emissions. This study introduces the latest research progress on bio-inspired microstructured surfaces in the field of underwater drag reduction, focusing on analyzing the drag reduction mechanism, preparation process, and application effect of the three major technological paths; namely, bio-inspired non-smooth surfaces, bio-inspired superhydrophobic surfaces, and bio-inspired modified coatings. Bio-inspired non-smooth surfaces can significantly reduce the wall shear stress by regulating the flow characteristics of the turbulent boundary layer through microstructure design. Bio-inspired superhydrophobic surfaces form stable gas–liquid interfaces through the construction of micro-nanostructures and reduce frictional resistance by utilizing the slip boundary effect. Bio-inspired modified coatings, on the other hand, realize the synergistic function of drag reduction and antifouling through targeted chemical modification of materials and design of micro-nanostructures. Although these technologies have made significant progress in drag reduction performance, their engineering applications still face bottlenecks such as manufacturing process complexity, gas layer stability, and durability. Future research should focus on the analysis of drag reduction mechanisms and optimization of material properties under multi-physical field coupling conditions, the development of efficient and low-cost manufacturing processes, and the enhancement of surface stability and adaptability through dynamic self-healing coatings and smart response materials. It is hoped that the latest research status of bio-inspired drag reduction technology reviewed in this study provides a theoretical basis and technical reference for the sustainable development and energy-saving design of ships and underwater vehicles. Full article

During the dry machining of 6061 aluminum alloy, cemented carbide tools often suffer from severe wear and built-up edge (BUE) formation, which significantly shortens tool life. Inspired by the non-smooth surface structure of dung beetles, this study proposes an elliptical dimple–groove composite bionic micro-texture, applied to the rake face of cemented carbide tools to enhance their cutting performance. Four types of tools with different surface textures were designed: non-textured (NT), single-groove texture (PT), circular dimple–groove composite texture (AKGC), and elliptical dimple–groove composite texture (TYGC). The cutting performance of these tools was analyzed through three-dimensional finite element simulations using the Deform-3D (version 11.0, Scientific Forming Technologies Corporation, Columbus, OH, USA) software program. The results showed that, compared to the NT tool, the TYGC tool exhibited the best performance, with a reduction in the main cutting force of approximately 30%, decreased tool wear, and significantly improved chip-breaking behavior. Based on the simulation results, a response surface model was constructed to optimize key texture parameters, and the optimal texture configuration was obtained. In addition, a theoretical model was developed to reveal the mechanism by which the micro-texture reduces interfacial friction and temperature rises by shortening the effective contact length. To verify the accuracy of the simulation and theoretical analysis, cutting experiments were further conducted. The experimental results were consistent with the simulation trends, and the TYGC tool demonstrated superior performance in terms of cutting force reduction, smaller adhesion area, and more stable cutting behavior, validating both the simulation model and the proposed texture design. This study provides a theoretical foundation for the structural optimization of bionic micro-textured cutting tools and offers an in-depth exploration of their friction-reducing and wear-resistant mechanisms, showing promising potential for practical engineering applications. Full article

Non-smooth, non-convex optimization problems frequently arise in modern machine learning applications, yet solving them efficiently remains a challenge. This paper addresses the minimization of functions of the form $f\left(x\right)={\sum }_{i=1}^m{f}_i\left(x\right)$ where each component is Lipschitz continuous but potentially non-smooth and non-convex. We extend the incremental subgradient method by incorporating weak subgradients, resulting in a framework better suited for non-convex objectives. We provide a comprehensive convergence analysis for three step size strategies: constant, diminishing, and a novel dynamic approach. Our theoretical results show that all variants converge to a neighborhood of the optimal solution, with the size of this neighborhood governed by the weak subgradient parameters. Numerical experiments on classification tasks with non-convex regularization, evaluated on the Breast Cancer Wisconsin dataset, demonstrate the effectiveness of the proposed approach. In particular, the dynamic step size method achieves superior practical performance, outperforming both classical and diminishing step size variants in terms of accuracy and convergence speed. These results position the incremental weak subgradient framework as a promising tool for scalable and efficient optimization in machine learning settings involving non-convex objectives. Full article

The Northeastern China Gravity Monitoring Network (NCGMN; 40–50°N), a pioneering time-variable gravity monitoring system in high-latitude cold-temperate environments, serves as a critical infrastructure for geodynamic investigations of the Songliao Basin, Changbai Mountain volcanic zone, and northern Tan-Lu Fault Zone. To address the data reliability challenges posed by nonlinear dynamic drifts in spring-type relative gravimeters during mobile surveys, this study quantifies—for the first time—the non-smooth normal distribution characteristics of such drifts using the inaugural 2015 dataset from two CG-5 instruments. Results demonstrate a 7–15% reduction in mean dynamic drift rates compared to static conditions, with spatiotemporal variability governed by multi-physics field coupling (terrain undulation, thermal fluctuation, and barometric perturbation). A comprehensive correction framework—integrating a gravimetric line drift rate computation, multi-model validation, and absolute datum cross-validation—reveals gravity value discrepancies up to ±10 μGal across models. The innovative hybrid scheme combines local drift preprocessing (initial-point modeling, line fitting, variance-sum optimization) with global adjustment optimization, achieving the significant suppression of nonlinear drift errors. The variance-sum optimal and Bayesian adjustment hybrid synergizes local variance minimization and global temporal correlation priors, delivering the following: (1) 34% and 29% reductions in segment self-difference standard deviations versus classical and Bayesian adjustments; (2) 24% and 14% decreases in segment residual standard deviations; (3) 12% and 6% improvements in absolute datum cross-validation precision. This study establishes a foundation for the reliable extraction of μGal-level gravity signals, advancing high-precision gravity monitoring of seismicity, volcanic unrest, and fault zone deformation in complex terrains. By harmonizing local-scale accuracy with network-wide consistency, the framework sets a new benchmark for time-variable gravity studies in challenging environments. Full article

In recent years, polycrystalline diamond compact (PDC) drill bits have seen significant advancements. They have replaced over 90% of the workload traditionally handled by roller cone bits and have become the predominant choice in energy drilling due to their superior efficiency and durability. However, PDC drill bits are susceptible to adhesion of rock cuttings during drilling in muddy formations, leading to mud accumulation on the bit surface. This phenomenon can cause drill bit failure and may contribute to downhole complications, including tool failure and borehole instability. The adhesion issue between PDC drill bits and mud rock cuttings underground is primarily influenced by the normal adhesion force between the drill bit surface and the mud rock cuttings. Therefore, biological non-smooth surface technology is applied to the prevention and control of drill bit balling. It is an optimal selection of biomimetic non-smooth surface structures with reduced adhesion and detachment properties. A non-smooth surface model for the PDC drill bit body is established through the analysis of the morphological characteristics of natural biological non-smooth surfaces. An experimental platform is designed and manufactured to evaluate the adhesion performance of non-smooth surface specimens. Indoor experiments are conducted to test the normal adhesion force of non-smooth surface specimens under varying morphologies, sizes, and contact times with clay. Finally, the anti-adhesion performance of the non-smooth surface unit structures is then analyzed. The normal adhesion force with a contact time of 12 h is as follows: 340 Pa of big square raised, 250 Pa of middle square raised, 190 Pa of small square raised, 315 Pa of big circular groove, 280 Pa of middle circular groove, 200 Pa of small circular groove, 225 Pa of big dot pit, 205 Pa of middle dot pit, and 130 Pa of small dot pit. Compared with the normal adhesion force of 550 Pa for smooth surface specimens with a contact time of 12 h, the anti-adhesion properties of the three non-smooth surface unit structure specimens designed in this paper were verified. We analyzed the anti-adhesion performance of non-smooth surface unit structures. At the critical contact time when the adhesion force tends to stabilize, the adhesion forces of different specimens are as follows: 330 Pa of big square raised, 237.5 Pa of middle square raised, 175 Pa of small square raised, 290 Pa of big circular groove, 250 Pa of middle circular groove, 160 Pa of small circular groove, 210 Pa of big dot pit, 185 Pa of middle dot pit, and 115 Pa of small dot pit. The results indicate that the anti-adhesion effect of small dot pit structures is the most effective, while the anti-adhesion effect of large square convex structures is the least effective. As the size of the unit structure decreases, it becomes more similar to the surface size of the organism. Additionally, a shorter contact time with clay leads to a better anti-adhesion effect. These findings provide new insights and research directions for the effective prevention and control of mud wrapping on PDC drill bits. Full article