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An improved proximal primal–dual ALM-based algorithm with convex combination proximal centers for equality-constrained convex programming in basis pursuit practical problems
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-01-30 DOI: 10.1016/j.cam.2025.116531
Xihong Yan , Hao Li , Chuanlong Wang , Danqing Zhou , Junfeng Yang
{"title":"An improved proximal primal–dual ALM-based algorithm with convex combination proximal centers for equality-constrained convex programming in basis pursuit practical problems","authors":"Xihong Yan ,&nbsp;Hao Li ,&nbsp;Chuanlong Wang ,&nbsp;Danqing Zhou ,&nbsp;Junfeng Yang","doi":"10.1016/j.cam.2025.116531","DOIUrl":"10.1016/j.cam.2025.116531","url":null,"abstract":"<div><div>In this paper, we propose a novel proximal point Lagrangian-based method for solving convex programming problems with linear equality constraints, where the proximal centers are constructed using convex combinations of the iterates. The new method preserves all the favorable characteristics of customized proximal point algorithm, including convergence of both the primal and dual iterates, as well as the ability to derive closed-form solutions for subproblems under certain conditions. Furthermore, we prove the global convergence and establish an <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mi>K</mi><mo>)</mo></mrow></mrow></math></span> ergodic sublinear convergence rate of our algorithm under mild assumptions. Finally, numerical experiments conducted on basis pursuit and equality-constrained quadratic programming problems demonstrate the superior performance of our proposed algorithm.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116531"},"PeriodicalIF":2.1,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143170292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An accelerated double-step derivative-free projection method based algorithm using Picard–Mann iterative process for solving convex constrained nonlinear equations
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-01-30 DOI: 10.1016/j.cam.2025.116541
J.K. Liu, B. Tang, T. Liu, Z.T. Yang, S. Liang
{"title":"An accelerated double-step derivative-free projection method based algorithm using Picard–Mann iterative process for solving convex constrained nonlinear equations","authors":"J.K. Liu,&nbsp;B. Tang,&nbsp;T. Liu,&nbsp;Z.T. Yang,&nbsp;S. Liang","doi":"10.1016/j.cam.2025.116541","DOIUrl":"10.1016/j.cam.2025.116541","url":null,"abstract":"<div><div>In this paper, we propose a double-step derivative-free projection method to solve large-scale nonlinear equations with convex constraints, which is an extension of the popular double direction and double-step method for solving unconstrained optimization problems. Its search direction contains the acceleration parameter and the correction parameter obtained by utilizing the approximate Jacobian matrix and the Picard–Mann hybrid iteration process, respectively. We prove the global convergence of the proposed method under the pseudo-monotone property of the mapping. Moreover, the R-linear convergence rate of the proposed method is presented. Numerical experiments verify the effectiveness of the proposed method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116541"},"PeriodicalIF":2.1,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143170294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spatially nonhomogeneous patterns for a modified Leslie–Gower model with predator-taxis
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-01-30 DOI: 10.1016/j.cam.2025.116542
Caijuan Jia, Yan Meng, Jiaxin Xiao
{"title":"Spatially nonhomogeneous patterns for a modified Leslie–Gower model with predator-taxis","authors":"Caijuan Jia,&nbsp;Yan Meng,&nbsp;Jiaxin Xiao","doi":"10.1016/j.cam.2025.116542","DOIUrl":"10.1016/j.cam.2025.116542","url":null,"abstract":"<div><div>In this paper, we investigate a modified Leslie–Gower predator–prey model with predator-taxis under the Neumann boundary condition. Firstly, the boundness of solution and the global stability conditions of the positive equilibrium are performed. Secondly, we take predator-taxis sensitivity coefficient as a potential bifurcation parameter for Turing bifurcation and analyze multiple steady-state bifurcation thresholds. Then, we use weak nonlinear analysis to derive amplitude equations to determine the direction of Turing bifurcation on multiple time scales. Finally, numerical simulations check the theoretical analysis results well. It is found that the predator-taxis can induce the occurrence of nonhomogeneous steady-state solution in space.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116542"},"PeriodicalIF":2.1,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143170293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Estimation of the covariance matrix of a Gaussian Markov Random Field under a total positivity constraint
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-01-30 DOI: 10.1016/j.cam.2025.116543
Juan Baz , Pedro Alonso , Juan Manuel Peña , Raúl Pérez-Fernández
{"title":"Estimation of the covariance matrix of a Gaussian Markov Random Field under a total positivity constraint","authors":"Juan Baz ,&nbsp;Pedro Alonso ,&nbsp;Juan Manuel Peña ,&nbsp;Raúl Pérez-Fernández","doi":"10.1016/j.cam.2025.116543","DOIUrl":"10.1016/j.cam.2025.116543","url":null,"abstract":"<div><div>Gaussian Markov Random Fields are a popular statistical model that has been used successfully in many fields of application. Recent work has studied conditions under which the covariance matrix of a Gaussian Markov Random Field over a graph of paths is totally positive. In such case, many linear algebra operations concerning the covariance matrix can be performed with High Relative Accuracy (the relative error is of order of machine precision). Unfortunately, classical estimators of the covariance matrix do not necessarily yield a totally positive matrix, even when the population covariance matrix is totally positive. Essentially, this inconvenience prevents the available High Relative Accuracy methods to be used with real-life data. Here, we present a method for the estimation of the covariance matrix of a Gaussian Markov Random Field over a graph of paths assuring the estimated covariance matrix (or its inverse) is totally positive.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116543"},"PeriodicalIF":2.1,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143170288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A matrix eigenvalue–eigenvector equality for semi-simple eigenvalues
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-01-26 DOI: 10.1016/j.cam.2025.116520
Huijian Zhu , Jiawen Ding , Jiu Ding
{"title":"A matrix eigenvalue–eigenvector equality for semi-simple eigenvalues","authors":"Huijian Zhu ,&nbsp;Jiawen Ding ,&nbsp;Jiu Ding","doi":"10.1016/j.cam.2025.116520","DOIUrl":"10.1016/j.cam.2025.116520","url":null,"abstract":"<div><div>For a complex square matrix, we present an eigenvalue–eigenvector equality for its semi-simple eigenvalue with a basis of the corresponding eigenspace under the condition that the eigenspace is orthogonal to eigenspaces or generalized eigenspaces corresponding to all other eigenvalues of the matrix. As a special case, we obtain a generalized eigenvector–eigenvalue-identity for the eigenvalue with an orthonormal basis of the eigenspace, which generalizes the well-known eigenvector–eigenvalue identity for a simple eigenvalue of normal matrices. We also give an application of the new formula to Jacobi matrices.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116520"},"PeriodicalIF":2.1,"publicationDate":"2025-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143170296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An efficient inertial projection-based algorithm for constrained nonlinear pseudo-monotone equations and its application to logistic regression problems
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-01-24 DOI: 10.1016/j.cam.2025.116532
Yong-Yan Yue , Teng-Teng Yao , Xiao-Qing Jin , Zhi Zhao
{"title":"An efficient inertial projection-based algorithm for constrained nonlinear pseudo-monotone equations and its application to logistic regression problems","authors":"Yong-Yan Yue ,&nbsp;Teng-Teng Yao ,&nbsp;Xiao-Qing Jin ,&nbsp;Zhi Zhao","doi":"10.1016/j.cam.2025.116532","DOIUrl":"10.1016/j.cam.2025.116532","url":null,"abstract":"<div><div>The problem of solving nonlinear pseudo-monotone equations with convex constraints is studied in this paper. To solve this problem, an adaptive hyperplane projection method is proposed. At each iteration, a diagonal Barzilai–Borwein method is used to construct search direction. For the hyperplane projection step, an extrapolation step is applied by using a nonmonotone line search technique. In addition, an inertial technique is applied for possible acceleration of this new algorithm. Under the assumptions that the underlying map is continuous and the solution set is nonempty, the proposed new algorithm is globally convergent. Moreover, if the Lipschitz continuity condition and the local error bound condition are also satisfied, then the new algorithm has a local linear convergence rate. Numerical experiments are reported to show the efficiency of the proposed method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116532"},"PeriodicalIF":2.1,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143169626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A fast generalized two-point homotopy perturbation iteration with a learned initial value for nonlinear ill-posed problems
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-01-24 DOI: 10.1016/j.cam.2025.116513
Xiaoyan Zhang, Guangyu Gao, Yang Li, Zhenwu Fu, Bo Han
{"title":"A fast generalized two-point homotopy perturbation iteration with a learned initial value for nonlinear ill-posed problems","authors":"Xiaoyan Zhang,&nbsp;Guangyu Gao,&nbsp;Yang Li,&nbsp;Zhenwu Fu,&nbsp;Bo Han","doi":"10.1016/j.cam.2025.116513","DOIUrl":"10.1016/j.cam.2025.116513","url":null,"abstract":"<div><div>In this paper, a new fast generalized iteration is proposed for solving nonlinear ill-posed problems in which forward operators may not be Gâteaux differentiable. We confirm that the generalized iteration constructed by the homotopy perturbation method and the two-point gradient method is an iterative regularization method. In addition, the physics-informed neural network is used to generate the initial value required for the iteration to converge faster and avoid falling into local minima. There is a key idea to use the modified discrete backtracking search algorithm to determine the combination parameters in each iteration. Since the forward operators may not be derivable in the process of theoretical analysis, we approximate it by the Bouligand sub-differential, which is proposed in Clason and Nhu (2019). The concept of asymptotic stability is introduced, which together with a generalized tangential cone condition proves the convergence and regularity of this method. Finally, several smooth and non-smooth numerical examples are carried out to demonstrate the efficiency and superior performance of the proposed method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116513"},"PeriodicalIF":2.1,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143170295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal conditions in uncertain set-valued optimization problems via second-order subdifferential involving Minkowski difference with application to zero-sum matrix games
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-01-23 DOI: 10.1016/j.cam.2025.116530
Yuwen Zhai , Guolin Yu , Tian Tang , Wenyan Han
{"title":"Optimal conditions in uncertain set-valued optimization problems via second-order subdifferential involving Minkowski difference with application to zero-sum matrix games","authors":"Yuwen Zhai ,&nbsp;Guolin Yu ,&nbsp;Tian Tang ,&nbsp;Wenyan Han","doi":"10.1016/j.cam.2025.116530","DOIUrl":"10.1016/j.cam.2025.116530","url":null,"abstract":"<div><div>The primary aim of this paper is to explore new ideas regarding second-order subdifferentials for set-valued maps, utilizing the framework of set order relations involving Minkowski difference. We commence by establishing fundamental properties of these subdifferentials, encompassing convexity, closure and the Moreau–Rockafellar theorem. Furthermore, existence theorems of the subdifferentials are derived. In addition, we establish optimality conditions of the <span><math><mi>m</mi></math></span>-order robust solutions to uncertain set optimization via the subdifferential. Moreover, we formulate duality theorems between the primal and the Wolfe dual problems. Finally, the paper concludes with an application of our current methodology to the context of two-player zero-sum matrix games.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116530"},"PeriodicalIF":2.1,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143170290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solving equilibrium and fixed-point problems in Hilbert spaces: A class of strongly convergent Mann-type dual-inertial subgradient extragradient methods
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-01-21 DOI: 10.1016/j.cam.2025.116509
Habib ur Rehman , Debdas Ghosh , Jen-Chih Yao , Xiaopeng Zhao
{"title":"Solving equilibrium and fixed-point problems in Hilbert spaces: A class of strongly convergent Mann-type dual-inertial subgradient extragradient methods","authors":"Habib ur Rehman ,&nbsp;Debdas Ghosh ,&nbsp;Jen-Chih Yao ,&nbsp;Xiaopeng Zhao","doi":"10.1016/j.cam.2025.116509","DOIUrl":"10.1016/j.cam.2025.116509","url":null,"abstract":"<div><div>This paper aims to enhance the convergence rate of the extragradient method by carefully selecting inertial parameters and employing an adaptive step-size rule. To achieve this, we introduce a new class of Mann-type subgradient extragradient methods that utilize a dual-inertial framework, applying distinct step-size formulas to generate the iterative sequence. Our main objective is to approximate a common solution to pseudomonotone equilibrium and fixed-point problems involving demicontractive mappings in real Hilbert spaces. The proposed methods integrate self-adaptive, monotone, and non-monotone step-size criteria, thereby eliminating the need to estimate Lipschitz-type constants. Under suitable conditions, we establish strong convergence theorems for the resulting iterative sequences. Moreover, we demonstrate the applicability of the proposed methods to both variational inequality and fixed-point problems. Numerical experiments confirm that these methods offer improved efficiency and performance compared to existing approaches in the literature.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116509"},"PeriodicalIF":2.1,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143170291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A linear and mass conservative scheme for the thermal soliton model based on nonlinear Schrödinger and heat transfer equations
IF 2.1 2区 数学
Journal of Computational and Applied Mathematics Pub Date : 2025-01-21 DOI: 10.1016/j.cam.2025.116529
Feng Guo , Weizhong Dai
{"title":"A linear and mass conservative scheme for the thermal soliton model based on nonlinear Schrödinger and heat transfer equations","authors":"Feng Guo ,&nbsp;Weizhong Dai","doi":"10.1016/j.cam.2025.116529","DOIUrl":"10.1016/j.cam.2025.116529","url":null,"abstract":"<div><div>A fully decoupled and mass-conservative finite difference (FD) scheme is proposed for solving the thermal soliton model which consists of a nonlinear Schrödinger (NLS) equation and a heat transfer equation, simulating soliton propagation through thermal medium. The scheme is proved to be uniquely solvable and unconditionally stable. Furthermore, the numerical solution is shown to be bounded and second-order convergent in <span><math><msub><mrow><mi>l</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> norm though the scheme has only the first-order spatial accuracy at the interfacial points. Several numerical examples are carried out to verify the theoretical analysis.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"464 ","pages":"Article 116529"},"PeriodicalIF":2.1,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143169625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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