Article
Computer Science, Interdisciplinary Applications
Mehdi Dehghan, Akbar Shirilord
Summary: This paper introduces seventh- and sixth-order methods for solving systems of nonlinear equations and provides convergence analysis. The computational efficiency of these methods is compared with Newton's method and other recently published methods. Numerical examples are included to demonstrate the validity and applicability of the methods and to compare them with existing results.
ENGINEERING WITH COMPUTERS
(2022)
Article
Mathematics, Interdisciplinary Applications
Bogdan Caruntu
Summary: The study used the Polynomial Least Squares Method to solve a class of fractional nonlinear integro-differential equations, demonstrating its simplicity and accuracy through comparisons with test problems.
FRACTAL AND FRACTIONAL
(2021)
Article
Automation & Control Systems
Chun Wei, Xiao Zhang, Ling Xu, Feng Ding, Erfu Yang
Summary: This article focuses on the parameter estimation problems for feedback nonlinear controlled autoregressive systems. It introduces a bilinear-in-parameter identification model and develops an overall recursive least squares algorithm and an overall stochastic gradient algorithm to handle the difficulties of bilinear parameters and reduce the computational burden. The convergence analysis of the algorithms is established using stochastic process theory, and simulation examples demonstrate the effectiveness of the proposed algorithms.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2022)
Article
Automation & Control Systems
Zhaobo Liu, Chanying Li
Summary: This article focuses on the stabilizability problem for a basic class of discrete-time nonlinear systems with multiple unknown parameters. It claims that such a system is stabilizable if its nonlinear growth rate is dominated by a polynomial rule, which is a necessary and sufficient condition when the system has a polynomial form. The article further proves that the concerned stabilizable system is possible to grow exponentially fast. Meanwhile, optimality and closed-loop identification are also discussed.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Review
Engineering, Multidisciplinary
Maolin Liang, Lifang Dai
Summary: Recent research on the multilinear system Axm-1=b with tensor A of order-m and dimension-n and vector b of dimension-n has focused on its applications in data mining, numerical PDEs, tensor complementary problems, etc. This paper introduces an alternating minimization method for solving this system and presents randomized versions to enhance performance, with numerical experiments demonstrating their superiority over existing methods in the same scenarios.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2021)
Article
Mathematics, Interdisciplinary Applications
P. Rahimkhani, Y. Ordokhani
Summary: The paper introduces an efficient method based on Chelyshkov polynomials and LS-SVR to solve a class of nonlinear stochastic differential equations. The method provides an effective solution for solving these equations and its superiority and efficiency are verified through test problems.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Computer Science, Information Systems
Xinyu Guo, Shifeng Ou, Menghua Jiang, Ying Gao, Jindong Xu, Zhuoran Cai
Summary: The newly proposed VSWS-KRLS algorithm incorporates basic pruning techniques and a window size adjustment mechanism to reduce computational complexity, improve convergence performance, and better track abrupt changes in the system on the basis of the traditional sliding window approach.
Article
Computer Science, Interdisciplinary Applications
Ali Shokri, Erfan Bahmani
Summary: This paper studies the coupled nonlinear sine-Gordon equations in liquid crystals and superconductors using MLPG and DMLPG methods. Results show that DMLPG methods are faster, more accurate, and more efficient than MLPG methods.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Mathematics, Applied
Z. El Majouti, R. El Jid, A. Hajjaj
Summary: The article expands the three-dimensional modified moving least-square method for solving high-dimensional linear and nonlinear integral equations, without the need for mesh connectivity, with support size having a significant effect on maximum errors. The MMLS method with a non-singular moment matrix achieves better results than MLS approximation, and numerical experiments demonstrate the differences between the two methods for multidimensional problems.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2022)
Article
Automation & Control Systems
Yan Ji, Zhen Kang, Xiao Zhang, Ling Xu
Summary: This paper focuses on the parameter and order estimation of multiple-input single-output nonlinear systems. By establishing a high-dimensional identification model and a sparse parameter vector, applying data filtering techniques, and using compressed sensing recovery theory, a data filtering-based orthogonal matching pursuit algorithm is proposed to accurately estimate the system parameters and orders from a small number of measurements.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Automation & Control Systems
Shuling Li, Wu Ai, Jian Wu, Quanxi Feng
Summary: This study introduces a fixed-time convergent algorithm for achieving distributed least square solutions of networked linear equations, with each agent in the network knowing only a subset of the equations and communicating with nearest neighbors. The settling time of the fixed-time distributed algorithm is independent of initial states and can be predetermined based on task requirements, as confirmed by numerical simulations.
INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS
(2021)
Article
Engineering, Electrical & Electronic
Abdul Wahab, Shujaat Khan, Imran Naseem, Jong Chul Ye
Summary: This article rigorously analyzes fractional learning algorithms, identifies key issues, and proposes solutions. Numerical experiments are conducted to verify the convergence and efficiency of fractional learning algorithms in stochastic environments. The conclusion is that fractional learning algorithms do not have an advantage over traditional least mean squares algorithms.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2022)
Article
Automation & Control Systems
Adam L. Bruce, Ankit Goel, Dennis S. Bernstein
Summary: In this paper, we introduce WPE as a direct generalization of PE that is necessary and sufficient for GAS in RLS. We explain how it can be understood as a non-uniform extension of PE to specific classes of summation windows and lower bound sequences. Furthermore, we show that WPE is equivalent to a condition that emerges from extending certain proofs of non-negative series divergence to sequences of real symmetric positive-semidefinite matrices.
SYSTEMS & CONTROL LETTERS
(2021)
Article
Engineering, Electrical & Electronic
Jing Chen, Manfeng Hu, Yanjun Liu, Quanmin Zhu
Summary: This study proposes two iterative reweighted (IRE) algorithms to handle data contaminated by outliers. By assigning suitable weights, unbiased parameter estimates can be obtained, and the outliers can be removed.
IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
(2023)
Article
Operations Research & Management Science
Yuning Yang
Summary: This paper investigates the application of alternating least squares in tensor canonical polyadic approximation. It demonstrates alternative conditions for global convergence by weakening the positive definiteness assumption and discusses its connection to the uniqueness of exact CP decomposition.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2023)
Article
Computer Science, Software Engineering
Nicholas I. M. Gould, Valeria Simoncini
OPTIMIZATION METHODS & SOFTWARE
(2020)
Article
Computer Science, Software Engineering
C. Cartis, N. I. M. Gould, Ph L. Toint
OPTIMIZATION METHODS & SOFTWARE
(2020)
Article
Computer Science, Software Engineering
Coralia Cartis, Nicholas I. M. Gould, Marius Lange
BIT NUMERICAL MATHEMATICS
(2020)
Article
Mathematics, Applied
Coralia Cartis, Nicholas I. M. Gould, Philippe L. Toint
SIAM JOURNAL ON OPTIMIZATION
(2020)
Article
Mathematics, Applied
Stefania Bellavia, Gianmarco Gurioli, Benedetta Morini
Summary: The approach utilizes adaptive regularization with cubics to solve nonconvex optimization problems, proposing a new variant based on dynamically chosen inexact Hessian information. The theoretical analysis of the proposed procedure ensures the key property of the ARC framework, which guarantees optimal worst-case function/derivative evaluation bounds for first- and second-order critical points. Additionally, the application to large-scale finite-sum minimization based on subsampled Hessian is discussed and analyzed in a deterministic and probabilistic manner, supported by numerical experiments on synthetic and real datasets.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2021)
Article
Mathematics, Applied
S. Bellavia, M. Donatelli, E. Riccietti
Article
Operations Research & Management Science
Stefania Bellavia, Gianmarco Gurioli
Summary: This study adapts the adaptive cubic regularization method with dynamic inexact Hessian information for nonconvex optimization to the stochastic optimization setting. The research shows that using inexact first- and second-order derivatives can be beneficial in terms of computational savings.
Article
Computer Science, Theory & Methods
S. Bellavia, G. Gurioli, B. Morini, Ph. L. Toint
Summary: An algorithm for computing approximate local critical points of smooth unconstrained optimization problems is proposed, allowing random noise in derivatives and inexact function values. Bounds on the number of function and derivatives evaluations are established based on the optimization order q relative to the p-th derivative, with the accuracy of these bounds depending on whether q is greater than 2 or less than 2. The extension to convexly constrained problems is also outlined, with these bounds being sharp in terms of accuracy tolerances.
JOURNAL OF COMPLEXITY
(2022)
Article
Mathematics, Applied
Enrico Meli, Benedetta Morini, Margherita Porcelli, Cristina Sgattoni
Summary: Spectral residual methods are derivative-free and low-cost procedures for solving nonlinear systems of equations. They compare well with Newton-based methods for large nonlinear systems and sequences. This work addresses the selection of steplength both theoretically and experimentally, providing results on real application like rolling contact problem.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Stefania Bellavia, Jacek Gondzio, Margherita Porcelli
Summary: This paper introduces a new relaxed variant of interior point method for low-rank semidefinite programming problems, imposing a special nearly low-rank form of all primal iterates and approximating the first order optimality conditions by solving an auxiliary least-squares problem. The method allows for the computation of both primal and dual approximated Newton directions, and its convergence has been established, with promising preliminary computational results for solving SDP-reformulation of matrix-completion problems.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Operations Research & Management Science
Stefania Bellavia, Natasa Krejic, Benedetta Morini, Simone Rebegoldi
Summary: The proposed method introduces a stochastic first-order trust-region method that combines inexact restoration approach, trust-region procedure, and random models for solving finite-sum minimization problems. The algorithm improves feasibility and optimality in a modular manner and reduces the expected number of iterations for reaching a near-stationary point by imposing probability accuracy requirements on random functions and gradients.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2023)
Article
Operations Research & Management Science
Stefania Bellavia, Gianmarco Gurioli, Benedetta Morini, Philippe Louis Toint
Summary: This paper discusses the problem of premature termination of optimization algorithms due to intrinsic noise in objective function and derivatives evaluations, and presents evaluation complexity bounds considering this situation. The results show that the presence of intrinsic noise may dominate these bounds, in contrast with what is known for methods in which the inexactness in function and derivatives' evaluations is fully controllable. Moreover, the new analysis provides estimates of the optimality level achievable, should noise cause early termination. Numerical experiments are reported that support the theory. The analysis finally sheds some light on the impact of inexact computer arithmetic on evaluation complexity.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Stefania Bellavia, Benedetta Morini, Simone Rebegoldi
Summary: This paper studies the convergence properties of SIRTR, a stochastic inexact restoration trust-region method for minimizing a finite sum of continuously differentiable functions. The method combines the trust-region methodology with random function and gradient estimates formed by subsampling. In contrast to other existing schemes, it enforces the decrease of a merit function by combining function approximation with an infeasibility term. The paper provides a convergence analysis and proves the convergence in probability of SIRTR under suitable accuracy requirements on random function and gradient estimates. Numerical results on nonconvex classification test problems are also reported, discussing the impact of probabilistic requirements on sample size selection.
Article
Operations Research & Management Science
S. Bellavia, G. Gurioli, B. Morini, Ph. L. Toint
Summary: This paper presents a trust-region algorithm for finding approximate minimizers of smooth unconstrained functions with random noise. The method finds an epsilon-approximate minimizer of any order q >= 1 with a small number of inexact evaluations of the function and its derivatives, based on suitable probabilistic assumptions. The impact of intrinsic noise and the failure of assumptions on the algorithm's performance are discussed, particularly in the case of large gradients. The paper also discusses and illustrates the conclusions in the context of subsampling methods for finite-sum optimization.
EURO JOURNAL ON COMPUTATIONAL OPTIMIZATION
(2022)
Proceedings Paper
Computer Science, Interdisciplinary Applications
Stefania Bellavia, Gianmarco Gurioli, Benedetta Morini, Philippe L. Toint
Summary: This paper focuses on regularisation methods using up to third order models to search for up to second-order critical points of a finite-sum minimisation problem. The expected number of iterations matches the worst-case optimal complexity for the deterministic counterpart of the method, and preliminary numerical tests in the context of nonconvex binary classification have been presented.
2021 21ST INTERNATIONAL CONFERENCE ON COMPUTATIONAL SCIENCE AND ITS APPLICATIONS ICCSA 2021
(2021)
