Zhihua Allen-Zhao

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.

We propose a stochastic minimization model to find a robust solution of a system of stochastic vertical linear complementarity problems. This model aims to minimize a risk function under stochastic vertical linear complementarity constraints. We reformulate the model with a finite support set as a linearly constrained piecewise smooth minimization problem by a penalty method. We prove the existence of exact penalty parameters regarding global and local minimizers. We define a smoothing function of the piecewise smooth objective function and show that the smoothing function satisfies the Kurdyka–Łojasiewicz (KL) property. Moreover, we propose a smoothing block coordinate descent algorithm and prove that the sequence generated by the algorithm globally converges to an [ ]-Clarke stationary point of the penalty problem by the KL property for any [ ]. Finally, we apply our model and algorithm to portfolio selection problems with real data. Numerical results demonstrate the robustness of our model. Funding: X. Chen was supported in part by the Hong Kong Research Grant Council [Grants PolyU15300123, and PolyU15300322] and the CAS-Croucher Funding Scheme for the AMSS-PolyU Joint Laboratory. Z. Allen-Zhao was supported in part by the National Natural Science Foundation of China [Grant 12301405], the Shaanxi Fundamental Science Research Project for Mathematics and Physics [Grant 23JSZ010], and the Fundamental Research Fund for Central Universities of China [Grant ZYTS25201].

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., $\ell_0$-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.

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.

Multiview clustering, an unsupervised learning method, has gained significant attention. In this paper, we investigate a multiview clustering methodology using sparse optimization. A featured difference from the existing literatures is the synergy of the two types of sparse constraints. Specially, we employ the cardinality (also known as L0-norm) constraints to extract reliable structure information of the original data, and the low-rank constraint to reveal a coherent structure within the consensus affinity matrix. As a result, we propose a novel cardinality-constrained low rank least squares regression (CL-LSR) model for multiview subspace clustering. To solve the CL-LSR model, we develop an efficient alternating quadratic penalty (AQP) method, where two sparse non-convex subproblems are alternately solved at each iteration, each having explicit iterations. We also provide a rigorous convergence analysis. Finally, empirical tests on various data sets are presented to demonstrate the superior performance of our proposed method.

In this paper, we investigate an enhanced indexation methodology using robust Conditional Value-at-Risk (CVaR) and group-sparse optimization. A featured difference from the existing literatures is to describe the tail risk using the worst-case CVaR of excess returns (WCVaR-ER), and the process of industry selection using a weighted $\ell_{\infty,1}$-norm constraint. We develop an accelerated alternating minimization algorithm (AMA) for solving this problem. At each iteration, this method usually alternately solves a convex cone program, which admits a closed-form solution via convex duality theory, and a projection problem onto a weighted infinity-to-one-ball, where a fixed-point iteration projection method is developed, terminating in finite number of iterations. The global convergence rates in terms of the primal and dual residuals are also provided. Empirical tests on actual data sets are presented to demonstrate the superior out-of-sample performance of our proposed strategy.