For non-convex functions where derivative information is difficult to obtain, escaping saddle points remains a significant challenge. Existing zeroth-order optimization algorithms approximate the true gradient using unbiased gradient estimation techniques, employing zero-mean random perturbations, or exploring negative curvature directions to escape saddle points. However, these methods encounter near-zero approximate gradients in the vicinity of saddle points, necessitating multiple small perturbations to escape, thereby consuming a substantial number of function evaluations. In this work, we propose the Two-step Simultaneous Perturbation Stochastic Approximation (2-SPSA) approach, to facilitate saddle point escape, which requires fewer function evaluations. At each iteration, this method requires only 4 function evaluations to estimate the gradients at the current point and its neighboring point, of which their convex combination serves as the descent direction. The randomness inherent in this gradient estimation aids in rapidly jumping out of saddle points. Experimental results indicate that the proposed method can escape saddle points with fewer function evaluations compared to other zeroth-order optimization algorithms.

This paper proposes a finite-time distributed semi-supervised learning (FTDSSL) algorithm based on the zero-gradient-sum strategy, manifold regularization, and extreme learning machines. The FTDSSL algorithm is designed for addressing distributed learning problems involving distributed data, including unlabeled samples. Thanks to the ZGS strategy, it yields results comparable to semi-supervised learning algorithms using single-layer feedforward neural networks on the full dataset. Moreover, FTDSSL exhibits convergence within a finite number of iterations. Each FTDSSL iteration shares only updated output weights between neighbors, preserving data privacy and communication bandwidth. Theoretical underpinnings, as exemplified by Theorem 1, demonstrate the global convergence of the FTDSSL algorithm through Lyapunov theory. Compared to event-triggered distributed semi-supervised learning, FTDSSL significantly reduces iteration count rather than communication volume. Experimental results validate that the FTDSSL algorithm converges within a finite time frame and proves efficient for distributed learning, particularly on datasets that include unlabeled samples.

To address the persistent challenge of balancing diversity preservation and convergence acceleration in metaheuristic optimization, we introduce MLS-JAYA - an enhanced algorithm incorporating several learning mechanisms. The proposed approach integrates population-based incremental learning to model promising solution distributions, a refined search operator for accelerated convergence, and orthogonal opposition-based learning to prevent premature stagnation. Comprehensive evaluation on the CEC2017 benchmark suite and six mechanical engineering design problems demonstrates MLS-JAYA’s competitive performance. Practical application in wireless sensor network (WSN) node coverage optimization further validates its effectiveness. Comparative analysis against four JAYA variants and other state-of-the-art metaheuristics confirms the algorithm’s superior optimization capabilities across diverse problem domains. The source code of MLS-JAYA is publicly available at https://github.com/denglingyun123/MLS-JAYA .

Partial Multi-Label Learning (PML) is a weakly-supervised learning framework where each training instance is associated with multiple candidate labels, only a subset of which are valid. The primary challenge in PML lies in effectively distinguishing ground-truth labels from noisy candidates, which becomes particularly acute in text categorization tasks due to the inherent sparsity of feature representations. To address these challenges, this paper proposes Partial Multi-Label Learning with Sparse Data (PML-SD), a novel approach that integrates low-rank and sparse decomposition of the feature matrix. Specifically, we formulate a unified optimization framework that combines trace norm regularization to capture low-rank structures and l1-norm regularization to induce sparsity. The ground-truth labels are recovered through joint minimization of label prediction loss and regularization terms, with the optimization problem being efficiently solved using the Augmented Lagrange Multiplier (ALM) algorithm. To validate our approach, extensive experiments demonstrate that PML-SD consistently outperforms state-of-the-art methods across multiple evaluation metrics, particularly in scenarios with high feature sparsity and label noise.

Vegetation patterns in arid and semi-arid regions exhibit diverse spatial structures that reflect ecosystem dynamics and functioning. Although vegetation-water interaction models have been widely studied, the effect of delayed nonlocal uptake has been explored mainly in specific model settings. Its role within the reduced Zelnik-type uptake-diffusion framework has received less systematic attention. In this study, we extend the reduced vegetation-water model proposed by Zelnik et al. by incorporating a phenomenological delayed nonlocal water-availability term. Based on this extended model, we perform a theoretical analysis to derive the conditions for Turing instability and apply multiple-scale analysis to obtain the corresponding amplitude equations near the bifurcation threshold. The stability of these amplitude equations is further investigated to characterize the emergence of stripe, spot, and mixed patterns. Numerical simulations are carried out to verify the analytical results and illustrate the evolution of vegetation patterns under different parameter regimes. The results demonstrate that, within appropriate parameter ranges, uniform vegetation states can undergo transitions to gap patterns, thereby providing a model-based perspective on degradation-related pattern transitions within this framework.

The efficiency of the classic proximal gradient method (PGM) in solving structured convex optimization problems depends on properly selected step sizes. We present and test a predicted and corrected strategy for selecting step sizes that are predicted accurately by utilizing the local curvature of the gradient of the smooth function and controlling its increasing rate, and subsequently corrected using linesearch. With this step size strategy, we establish the convergence and convergence rate of the classic PGM in terms of the sequence of function values. Furthermore, we find that this proposed method is effective for some nonconvex regularization problems provided that the whole objective function is convex. Numerical experiments on well-known problems such as smoothed clipped absolute deviation penalty, sparse logistic regression, and quadratic minimization demonstrate that the predicted step size is satisfactory for all tested problems, thereby requiring few or even no linesearches to correct step sizes.

This article investigates the stability of delayed generalized neural networks (GNNs). First, a high-degree reciprocally convex inequality (RCI) is introduced, offering a novel method for estimating the lower bound of the reciprocally convex combination (RCC). This high-degree RCI subsumes several representative results as special cases. Second, to leverage the advantages of the high-degree RCI, a new Lyapunov-Krasovskii functional (LKF) in accordance with the application of high-degree RCI of order $r=3$ is constructed. Based on the high-degree RCI and the novel LKF, a less conservative delay-dependent stability criterion is derived to ensure the asymptotic stability of delayed GNNs. Third, four widely adopted numerical examples and a study on a real-world quadruple-tank process have been conducted to demonstrate the validity and merits of the new stability criterion.

Classical integer-order chaotic maps usually exhibit chaotic degradation under prolonged iterations or finite-precision computation, which may compromise the reliability of chaos-based algorithms. Fractional difference chaotic systems with memory effects offer a promising alternative; however, existing studies rarely provide a systematic and quantitative understanding of how the nonlinear gain parameter, memory strength, and initial condition collectively influence the emergence and robustness of complex dynamics under finite-time iterations. It should be noted that memory effects do not inherently guarantee robust chaotic behavior under finite-precision computation, and appropriate parameter and initial-condition selection remains essential. In this paper, we conduct a systematic numerical dynamical analysis of a logistic-type fractional difference system with power-law memory by leveraging bifurcation diagrams and Lyapunov exponent mappings. Rather than aiming to select optimal parameter points, we propose a quantitative composite chaos evaluation (CCE) framework to identify admissible parameter intervals within which robust finite-time chaotic dynamics can be consistently sustained. Numerical results demonstrate the effectiveness and reliability of the proposed framework, which may facilitate future applications in chaos-enhanced optimization, nonlinear control, and secure communication.

A multiprocessor system is classified as t/s-diagnosable if it is possible to pinpoint all malfunctioning processors within a group of no more than s processors, assuming the total number of faults does not surpass t. The notion of t/(t + 1)-diagnosability represents the highest value of k for which the system is considered k/(k + 1)-diagnosable. This metric has received considerable attention in prior research concerning various multiprocessor systems. This paper's significant contributions include introducing a necessary and sufficient criterion for t/(t + 1)-diagnosability of multiprocessor systems under the PMC model. Moreover, we assess the t/(t + 1)-diagnosability for an n-dimensional alternating group graph AGn within the same model. Specifically, we find that the diagnosability of AG4 is 5, AG5 is 13, and for n >= 6, the diagnosability of AGn is 6n-16.

This paper investigates the stability and stabilization problems for T-S fuzzy systems with two stochastic additive time-varying delays. By taking full account of the stochastic characteristics of these delays, the original system is equivalently reformulated into a new system representation. In contrast to existing works, a controller accounting for two stochastic additive delays is designed using a delay partitioning approach. Subsequently, a structurally simple Lyapunov-Krasovskii functional (LKF) is constructed to effectively utilize the information regarding two stochastic time-varying delays and their derivatives. Based on this LKF, novel delay-derivative/distribution-dependent stability and stabilization criteria are derived, which are less conservative compared to previous results. Finally, the advantages and effectiveness of the proposed methods are demonstrated through three widely used numerical examples and a practical truck-trailer system.

We are concerned with the global behavior of positive solutions for some classes of semipositone third-order nonlinear boundary value problems u ''' = lambda f (t, u), t is an element of (0, 1), u(0) = u '(eta) = 0, u ''(1) +g(u(1))u(1) = 0, where eta is an element of((1)(2), 1), lambda is a positive parameter, g is an element of C([0, infinity), [0, infinity)) and f is an element of C([0, 1] & times; [0, infinity), ) with f (t, 0) <0. The proof of our main results are based upon bifurcation theory.

Although differential evolution (DE) has demonstrated strong capability in handling numerical optimization and real world constrained problems, it still suffers from inherent limitations, including slow convergence and insufficient solution accuracy. To overcome these challenges, we propose a novel variant termed GDDE, which integrates principles from evolutionary game theory and feature selection into the traditional DE framework. Inspired by evolutionary game theory, the population is partitioned into two distinct sub-populations. A behavior driven payoff matrix is constructed to regulate strategic interactions between subpopulations, thereby adaptively guiding and stimulating evolutionary dynamics. Furthermore, drawing inspiration from feature selection, we introduce a dimensional complementarity crossover mechanism between the mutation vector and the target vector, replacing the conventional one. The performance of GDDE is comprehensively evaluated on CEC2017, CEC2022, eight large-scale optimization problems, nineteen constrained mechanical engineering problems, and a 3-dimensional UAV path planning task. The experimental results show that the proposed approach has significantly improved optimization performance compared to DE. Moreover, comparisons with fourteen state-of-the-art algorithms demonstrate the superior effectiveness, robustness, and practical applicability of GDDE, as evidenced by statistically significant improvements in mean error and standard deviation, with all results validated using non-parametric statistical tests (Wilcoxon signed rank, Holm-Bonferroni correction, Cliff’s delta and Friedman tests). The source code of GDDE is publicly available at https://github.com/Momo-pob/GDDE_code.git.

Network disintegration, which aims to degrade network functionality through the optimal set of node or edge removals, has been widely applied in various domains such as epidemic control and rumor containment. Hypernetworks are crucial and ubiquitous in capturing complex real- world higher-order interactions. However, existing network disintegration methods primarily focus on traditional pairwise networks, facing two significant challenges when dealing with hypernetworks: ineffective disruption of higher-order structures and limited capability in capturing higher-order features. To address these issues, we propose the Pre-Elite Multi-Objective Evolutionary Algorithm (PEEA), which identifies critical hyperedge set by optimizing two objectives: overall structure and higher-order disintegration. PEEA introduces weighted line graph to capture inter-hyperedge topological relationships and designs multi-scale importance metrics. It incorporates prior network information for elite individual initialization and optimizes target hyperedge set through multi-dimensional updates and selection operations. Simulation results show that PEEA improves the two objectives by 45.852% and 73.476%, demonstrating its effectiveness in hypernetwork disintegration. Further analysis of iterations (T) and crossover rate (beta) indicates that PEEA achieves its most significant improvement in the first iteration, balancing fast convergence with accuracy.

In this work, we design an efficient method for tackling the robust tensor completion problem. Tensor nuclear norm (TNN) is a conventional approach to solve the robust tensor completion problem. However, TNN may yield suboptimal solutions because the tensor rank is non-convex. With this purpose, we introduce an innovative tensor rank approximation that combines the Schatten-p norm with the Smoothly Clipped Absolute Deviation function. Additionally, we incorporate the Total Variation technique into the model to preserve the local smoothing properties of the image. To address the resulting model, we formulate a symmetric Alternating Direction Method of Multipliers algorithm (ADMM). Under some mild conditions, we validate that the solution produced by the algorithm converges to the KKT point of the model. Comprehensive experiments indicate the excellent performance of the proposed approach.

In this paper, we consider the symmetric cone linear complementarity problem with the Cartesian P 0 -property and present a regularization smoothing method with a nonmonotone line search to solve this problem. It has been demonstrated that the proposed method exhibits global convergence under the condition that the solution set of the complementarity problem is nonempty. This condition is less stringent than those that have appeared in some existing literature. We also show that the method has locally quadratic convergence under appropriate conditions. Some experimental results are reported to illustrate the efficiency of the proposed method.

Accurate parameter identification in photovoltaic (PV) models is crucial for performance evaluation but remains challenging due to their nonlinear, multimodal, and high-dimensional nature. Although the Dung Beetle Optimization (DBO) algorithm has shown potential in addressing such problems, it often suffers from premature convergence. To overcome these issues, this paper proposes a Memory Enhanced Fractional-Order Dung Beetle Optimization (MFO-DBO) algorithm that integrates three coordinated strategies. Firstly, fractional-order (FO) calculus introduces memory into the search process, enhancing convergence stability and solution quality. Secondly, a fractional-order logistic chaotic map improves population diversity during initialization. Thirdly, a chaotic perturbation mechanism helps elite solutions escape local optima. Numerical results on the CEC2017 benchmark suite and the PV parameter identification problem demonstrate that MFO-DBO consistently outperforms advanced DBO variants, CEC competition winners, FO-based optimizers, enhanced classical algorithms, and recent metaheuristics in terms of accuracy, robustness, convergence speed, while also maintaining an excellent balance between exploration and exploitation compared to the standard DBO algorithm.

This paper proposes a sparse optimization algorithm for robust learning in Multi-Agent Systems (MAS) based on the alternating direction method of multipliers (ADMM) named Huber-DRLSP by reasonably defining the global loss function. The algorithm focuses on solving machine learning (ML) problems of distributed data or large-scale data that contain noisy data. Furthermore, by incorporating a sparse penalty term, the algorithm gains feature selection capabilities, improving its generalization performance. The theoretical analysis provides an explicit relationship between utility and penalty parameters, along with a linear convergence rate of $O(1/K)$, where $K$ represents the number of iterations. The simulation results verify the theoretical findings and demonstrate the robustness and effectiveness of the algorithm.

This paper is concerned with the monotone stochastic tensor complementarity problem, where the expectation of the involved stochastic tensor is a strictly positive semi-definite tensor. At first, a new class of restricted nonlinear complementarity problem (NCP) function is defined by using the special structure of strictly semi-definite tensor. Then the conditional value at risk stochastic programming (CVaR-SP) model of monotone stochastic tensor complementarity problem (STCP) is established by taking the minimum value of the stochastic residual defined by the modified restricted NCP function as objective function, the nonnegativity of the variable and the CVaR inequality representing the feasibility conditions as constraint conditions. Next, the sample average approximation problem of the CVaR-SP model is presented by using the Monte Carlo method and the smoothing method. Subsequently, the conditions for the convergence of the sample average approximation problem are analyzed. Finally, the penalized sample average approximation algorithm is used to solve the problem, the related numerical results further verify the validity of the method.

Multiview clustering (MC) aims to group samples using consistent and complementary information across various views. The subspace clustering, as a fundamental technique of MC, has attracted significant attention. In this paper, we propose a novel joint sparse self-representation learning model for MC, where a featured difference is the extraction of view-specific local information by introducing cardinality (i.e., ℓ_0-norm) constraints instead of Graph-Laplacian regularization. Specifically, under each view, cardinality constraints directly restrict the samples used in the self-representation stage to extract reliable local and global structure information, while the low-rank constraint aids in revealing a global coherent structure in the consensus affinity matrix during merging. The attendant challenge is that Augmented Lagrange Method (ALM)-based alternating minimization algorithms cannot guarantee convergence when applied directly to our nonconvex, nonsmooth model, thus resulting in poor generalization ability. To address it, we develop an alternating quadratic penalty (AQP) method with global convergence, where two subproblems are iteratively solved by closed-form solutions. Empirical results on six standard datasets demonstrate the superiority of our model and AQP method, compared to eight state-of-the-art algorithms.