Pub Date : 2026-10-01Epub Date: 2026-02-17DOI: 10.1016/j.cam.2026.117451
Doulaye Dembélé
The singular value decomposition (SVD) allows to write a matrix as a product of a left singular vectors matrix, a nonnegative singular values diagonal matrix and a right singular vectors matrix. Among the applications of the SVD are the principal component analysis, the low-rank matrix approximation and the solving of a linear system of equations. The methods used for computing this decomposition allow to get the complete or partial result. For very large size matrix, the probabilistic methods allow to get partial result by using less computational load. A power method is proposed in this paper for computing all or the k first largest SVD subspaces for a real-valued matrix. The k first right singular vectors of this method are the k columns of a neural network encoder weight matrix. The accuracy of this iterative search method depends on the behavior of the singular values and the settings of the gradient search optimizer used. A R package implementing the proposed method is available at https://cran.r-project.org/web/packages/psvd/index.html.
{"title":"A power method for computing singular value decomposition","authors":"Doulaye Dembélé","doi":"10.1016/j.cam.2026.117451","DOIUrl":"10.1016/j.cam.2026.117451","url":null,"abstract":"<div><div>The singular value decomposition (SVD) allows to write a matrix as a product of a left singular vectors matrix, a nonnegative singular values diagonal matrix and a right singular vectors matrix. Among the applications of the SVD are the principal component analysis, the low-rank matrix approximation and the solving of a linear system of equations. The methods used for computing this decomposition allow to get the complete or partial result. For very large size matrix, the probabilistic methods allow to get partial result by using less computational load. A power method is proposed in this paper for computing all or the <em>k</em> first largest SVD subspaces for a real-valued matrix. The <em>k</em> first right singular vectors of this method are the <em>k</em> columns of a neural network encoder weight matrix. The accuracy of this iterative search method depends on the behavior of the singular values and the settings of the gradient search optimizer used. A R package implementing the proposed method is available at <span><span>https://cran.r-project.org/web/packages/psvd/index.html</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117451"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387125","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}
Pub Date : 2026-10-01Epub Date: 2026-02-22DOI: 10.1016/j.cam.2026.117507
Nguyen Song Ha , Simeon Reich , Truong Minh Tuyen , Pham Thi Thu
We study the mixed split feasibility problem in real Hilbert space. In order to find a solution to this problem, we use hybrid and shrinking projection methods to propose two new inertial multistep projection-type algorithms. A distinctive feature of our methods is that the inertial parameters are only required to be bounded, rather than diminishing or constrained to lie within fixed intervals such as or [0, a], as is commonly imposed in many existing inertial schemes. This relaxation makes the selection of inertial factors more flexible and easier to implement while still ensuring strong convergence. In addition, the other control parameters are selected so that the implementation of our algorithm does not depend on any prior information regarding the norms of the transfer operators.
{"title":"Two inertial multistep projection-type algorithms for solving mixed split feasibility problems in Hilbert space","authors":"Nguyen Song Ha , Simeon Reich , Truong Minh Tuyen , Pham Thi Thu","doi":"10.1016/j.cam.2026.117507","DOIUrl":"10.1016/j.cam.2026.117507","url":null,"abstract":"<div><div>We study the mixed split feasibility problem in real Hilbert space. In order to find a solution to this problem, we use hybrid and shrinking projection methods to propose two new inertial multistep projection-type algorithms. A distinctive feature of our methods is that the inertial parameters are only required to be bounded, rather than diminishing or constrained to lie within fixed intervals such as <span><math><mrow><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span> or [0, <em>a</em>], as is commonly imposed in many existing inertial schemes. This relaxation makes the selection of inertial factors more flexible and easier to implement while still ensuring strong convergence. In addition, the other control parameters are selected so that the implementation of our algorithm does not depend on any prior information regarding the norms of the transfer operators.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117507"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386630","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}
Pub Date : 2026-10-01Epub Date: 2026-02-11DOI: 10.1016/j.cam.2026.117430
Mostafa M.A. Khater
This article presents a comprehensive analytical and dynamical investigation of a nonlinear long-wave model in which wave propagation is governed by the interplay of nonlinear steepening, regularizing dispersion, linear drift and a second-order term controlled by the parameter ϱ. The sign of ϱ determines the physical regime of the medium: (ϱ > 0) corresponds to weak dissipation, recovers a nondissipative or conservative propagation environment, while (ϱ < 0) models an anti-dissipative or energy-feeding regime in which small disturbances may grow. Such a structure captures a wide range of physical situations including unidirectional shallow-water waves, weakly viscous channels and long-wave transport in media where energy may be damped, conserved, or injected. Using the Khater II technique, we construct new explicit traveling-wave solutions such as solitary, periodic and kink-type profiles. The traveling-wave reduction is rewritten as a Hamiltonian system, enabling a detailed stability analysis and a qualitative description of the phase-space geometry. A full bifurcation classification is provided, distinguishing periodic, homoclinic and heteroclinic orbits across different parameter regimes. To investigate sensitivity to external fluctuations, a weak time-periodic perturbation is introduced, generating quasi-periodic and chaotic dynamics demonstrated through numerical simulations and Poincaré sections. The results reveal how dispersion, nonlinearity and the sign of ϱ jointly shape the onset of complex long-wave behavior and provide exact analytical benchmarks for validating numerical solvers in dissipative and non-dissipative dispersive systems.
{"title":"Bifurcation scenarios and quasi-periodic dynamics in a dispersive-dissipative medium","authors":"Mostafa M.A. Khater","doi":"10.1016/j.cam.2026.117430","DOIUrl":"10.1016/j.cam.2026.117430","url":null,"abstract":"<div><div>This article presents a comprehensive analytical and dynamical investigation of a nonlinear long-wave model in which wave propagation is governed by the interplay of nonlinear steepening, regularizing dispersion, linear drift and a second-order term controlled by the parameter ϱ. The sign of ϱ determines the physical regime of the medium: (ϱ > 0) corresponds to weak dissipation, <span><math><mrow><mo>(</mo><mi>ϱ</mi><mo>=</mo><mn>0</mn><mo>)</mo></mrow></math></span> recovers a nondissipative or conservative propagation environment, while (ϱ < 0) models an anti-dissipative or energy-feeding regime in which small disturbances may grow. Such a structure captures a wide range of physical situations including unidirectional shallow-water waves, weakly viscous channels and long-wave transport in media where energy may be damped, conserved, or injected. Using the Khater II technique, we construct new explicit traveling-wave solutions such as solitary, periodic and kink-type profiles. The traveling-wave reduction is rewritten as a Hamiltonian system, enabling a detailed stability analysis and a qualitative description of the phase-space geometry. A full bifurcation classification is provided, distinguishing periodic, homoclinic and heteroclinic orbits across different parameter regimes. To investigate sensitivity to external fluctuations, a weak time-periodic perturbation is introduced, generating quasi-periodic and chaotic dynamics demonstrated through numerical simulations and Poincaré sections. The results reveal how dispersion, nonlinearity and the sign of ϱ jointly shape the onset of complex long-wave behavior and provide exact analytical benchmarks for validating numerical solvers in dissipative and non-dissipative dispersive systems.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117430"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387121","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}
Pub Date : 2026-10-01Epub Date: 2026-02-17DOI: 10.1016/j.cam.2026.117463
Carlos A.R. Diniz , Jhonata Da Silva Pereira , Victor H. Lachos
We introduce a finite mixture of matrix-variate shifted generalized asymmetric Laplace (MVSGAL) distributions for clustering matrix-valued data with skewness and heavy tails. The model offers a flexible alternative to the matrix-variate normal benchmark by accommodating directional skewness (via a skewness matrix) and component-specific tail behavior while capturing row/column dependence. For completeness, we briefly summarize the MVSGAL kernel (density and stochastic representation with a fixed Gamma mixing law) and the conditional moments needed for estimation. We develop an Expectation-Conditional Maximization (ECM) algorithm for maximum-likelihood inference that uses latent component indicators and gamma-scale variables. A simulation study assesses parameter recovery and the impact of distributional misspecification. For the empirical illustration, we analyze a 10-year monthly series of climate data (temperature, precipitation, and solar radiation) from four municipalities in São Paulo, Brazil. The fitted model successfully identifies three distinct climatic regimes, capturing the data’s skewness, heavy tails, and dependencies in a parsimonious matrix-variate framework.
{"title":"Finite mixtures of matrix-variate shifted generalized asymmetric Laplace distribution for three-way data","authors":"Carlos A.R. Diniz , Jhonata Da Silva Pereira , Victor H. Lachos","doi":"10.1016/j.cam.2026.117463","DOIUrl":"10.1016/j.cam.2026.117463","url":null,"abstract":"<div><div>We introduce a finite mixture of matrix-variate shifted generalized asymmetric Laplace (MVSGAL) distributions for clustering matrix-valued data with skewness and heavy tails. The model offers a flexible alternative to the matrix-variate normal benchmark by accommodating directional skewness (via a skewness matrix) and component-specific tail behavior while capturing row/column dependence. For completeness, we briefly summarize the MVSGAL kernel (density and stochastic representation with a fixed Gamma mixing law) and the conditional moments needed for estimation. We develop an Expectation-Conditional Maximization (ECM) algorithm for maximum-likelihood inference that uses latent component indicators and gamma-scale variables. A simulation study assesses parameter recovery and the impact of distributional misspecification. For the empirical illustration, we analyze a 10-year monthly series of climate data (temperature, precipitation, and solar radiation) from four municipalities in São Paulo, Brazil. The fitted model successfully identifies three distinct climatic regimes, capturing the data’s skewness, heavy tails, and dependencies in a parsimonious matrix-variate framework.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117463"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387129","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}
Pub Date : 2026-10-01Epub Date: 2026-02-09DOI: 10.1016/j.cam.2026.117429
Zhenxian Luo , Haijun Xia , Linyuan Li
The topology optimization of continuum structures considering stress constraints is a classic hotspot. Recently, the Stress-Influence-Function with adaptive strength feature (SIF-ASF) approach was proposed for stress constrained continuum topology optimization. The stress influence function sets strong penalization on the local strength failure to achieve the stress constraints. However, this strong penalization may lead to oscillation or divergence due to a sharp barrier of the stress. In this study, an improved stress influence function, which has good boundedness and smoothness, is presented to alleviate nonlinearity in optimization and ensure numerical stability of optimization iterations. In addition, a new adaptive strategy for the strength feature factor is proposed to achieve good control on the maximum stress. By comparing with existing methods through two numerical examples, the advantages of the proposed method on numerical stability and weight reduction are verified. Finally, some useful conclusions are given objectively.
{"title":"An improved Stress-Influence-Function (ISIF) based method for continuum structural topology optimization with stress constraints","authors":"Zhenxian Luo , Haijun Xia , Linyuan Li","doi":"10.1016/j.cam.2026.117429","DOIUrl":"10.1016/j.cam.2026.117429","url":null,"abstract":"<div><div>The topology optimization of continuum structures considering stress constraints is a classic hotspot. Recently, the Stress-Influence-Function with adaptive strength feature (SIF-ASF) approach was proposed for stress constrained continuum topology optimization. The stress influence function sets strong penalization on the local strength failure to achieve the stress constraints. However, this strong penalization may lead to oscillation or divergence due to a sharp barrier of the stress. In this study, an improved stress influence function, which has good boundedness and smoothness, is presented to alleviate nonlinearity in optimization and ensure numerical stability of optimization iterations. In addition, a new adaptive strategy for the strength feature factor is proposed to achieve good control on the maximum stress. By comparing with existing methods through two numerical examples, the advantages of the proposed method on numerical stability and weight reduction are verified. Finally, some useful conclusions are given objectively.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117429"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387131","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}
Pub Date : 2026-10-01Epub Date: 2026-02-26DOI: 10.1016/j.cam.2026.117495
Minsheng Huang , Ruo Li , Kai Yan , Chengbao Yao , Wenjun Ying
The reference field method, known as the difference formulation, is a key variance reduction technique for Monte Carlo simulations of thermal radiation transport problems. When the material temperature is relatively high and the spatial temperature gradient is moderate, this method demonstrates significant advantages in reducing variance compared to classical Monte Carlo methods. However, in problems with larger temperature gradients, this method has not only been found ineffective at reducing statistical noise, but in some cases, it even increases noise compared to classical Monte Carlo methods. The global optimal reference field method, a recently proposed variance reduction technique, effectively reduces the average energy weight of Monte Carlo particles, thereby decreasing variance. Its effectiveness has been validated both theoretically and numerically, demonstrating a significant reduction in statistical errors for problems with large temperature gradients. In our previous work, instead of computing the exact global optimal reference field, we developed an approximate, physically motivated method to find a relatively better reference field using a selection scheme. In this work, we reformulate the problem of determining the global optimal reference field as a linear programming problem and solve it exactly. To further enhance computational efficiency, we use the MindOpt solver, which leverages graph neural network methods. Numerical experiments demonstrate that the MindOpt solver not only solves linear programming problems accurately but also significantly outperforms the Simplex and interior-point methods in terms of computational efficiency. The global optimal reference field method combined with the MindOpt solver not only improves computational efficiency but also substantially reduces statistical errors.
{"title":"An efficient Monte Carlo simulation for radiation transport based on global optimal reference field","authors":"Minsheng Huang , Ruo Li , Kai Yan , Chengbao Yao , Wenjun Ying","doi":"10.1016/j.cam.2026.117495","DOIUrl":"10.1016/j.cam.2026.117495","url":null,"abstract":"<div><div>The reference field method, known as the difference formulation, is a key variance reduction technique for Monte Carlo simulations of thermal radiation transport problems. When the material temperature is relatively high and the spatial temperature gradient is moderate, this method demonstrates significant advantages in reducing variance compared to classical Monte Carlo methods. However, in problems with larger temperature gradients, this method has not only been found ineffective at reducing statistical noise, but in some cases, it even increases noise compared to classical Monte Carlo methods. The global optimal reference field method, a recently proposed variance reduction technique, effectively reduces the average energy weight of Monte Carlo particles, thereby decreasing variance. Its effectiveness has been validated both theoretically and numerically, demonstrating a significant reduction in statistical errors for problems with large temperature gradients. In our previous work, instead of computing the exact global optimal reference field, we developed an approximate, physically motivated method to find a relatively better reference field using a selection scheme. In this work, we reformulate the problem of determining the global optimal reference field as a linear programming problem and solve it exactly. To further enhance computational efficiency, we use the MindOpt solver, which leverages graph neural network methods. Numerical experiments demonstrate that the MindOpt solver not only solves linear programming problems accurately but also significantly outperforms the Simplex and interior-point methods in terms of computational efficiency. The global optimal reference field method combined with the MindOpt solver not only improves computational efficiency but also substantially reduces statistical errors.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117495"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386903","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}
Pub Date : 2026-10-01Epub Date: 2026-02-21DOI: 10.1016/j.cam.2026.117474
Fangfang Shi , Guoju Ye , Wei Liu , Debdas Ghosh
The main objective of this paper is to investigate the KKT optimality condition for fuzzy optimization problems with inequality constraints. To begin with, by proving that the intersection of the cone of descent directions and the cone of feasible directions at the optimal point is an empty set, we establish the first-order optimality condition for unconstrained fuzzy optimization problems. On this basis, the Fritz-John optimality condition for fuzzy optimization problems with inequality constraints is derived through the fuzzy Gordan’s theorem. Furthermore, in order to ensure that the Lagrangian multipliers must satisfy not all zero, we strengthen the assumptions to deduce the KKT optimality condition. Meanwhile, some numerical examples are created to verify the validity of theoretical results. It is particularly worth mentioning that the optimality conditions established in this paper are such that zero belongs to a certain interval, which makes our results computationally superior than in the previous literature, where the optimality conditions are equalities. Finally, the developed optimality conditions are employed to address a binary classification problem related to support vector machines with fuzzy data.
{"title":"Optimality conditions for fuzzy optimization problems and its application to classification problems with fuzzy data","authors":"Fangfang Shi , Guoju Ye , Wei Liu , Debdas Ghosh","doi":"10.1016/j.cam.2026.117474","DOIUrl":"10.1016/j.cam.2026.117474","url":null,"abstract":"<div><div>The main objective of this paper is to investigate the KKT optimality condition for fuzzy optimization problems with inequality constraints. To begin with, by proving that the intersection of the cone of descent directions and the cone of feasible directions at the optimal point is an empty set, we establish the first-order optimality condition for unconstrained fuzzy optimization problems. On this basis, the Fritz-John optimality condition for fuzzy optimization problems with inequality constraints is derived through the fuzzy Gordan’s theorem. Furthermore, in order to ensure that the Lagrangian multipliers must satisfy not all zero, we strengthen the assumptions to deduce the KKT optimality condition. Meanwhile, some numerical examples are created to verify the validity of theoretical results. It is particularly worth mentioning that the optimality conditions established in this paper are such that zero belongs to a certain interval, which makes our results computationally superior than in the previous literature, where the optimality conditions are equalities. Finally, the developed optimality conditions are employed to address a binary classification problem related to support vector machines with fuzzy data.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117474"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386992","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}
Pub Date : 2026-10-01Epub Date: 2026-02-27DOI: 10.1016/j.cam.2026.117492
Xiao Peng , Yijing Wang , Zhiqiang Zuo
This paper explores the asymptotic leader-follower consensus and Mittag-Leffler leader-follower consensus for variable-order multi-agent systems in the presence of unknown nonlinearity and external disturbances. Under the fixed/switching topologies, sufficient consensus criteria are respectively developed by proposing non-switched/switched distributed adaptive neural network-based dynamic event-trigger control schemes. At the end of this paper, some numerical simulations and comparison results are presented to imply the effectiveness of the proposed control strategies.
{"title":"Leader-follower consensus for variable-order multi-agent systems with fixed/switching topologies","authors":"Xiao Peng , Yijing Wang , Zhiqiang Zuo","doi":"10.1016/j.cam.2026.117492","DOIUrl":"10.1016/j.cam.2026.117492","url":null,"abstract":"<div><div>This paper explores the asymptotic leader-follower consensus and Mittag-Leffler leader-follower consensus for variable-order multi-agent systems in the presence of unknown nonlinearity and external disturbances. Under the fixed/switching topologies, sufficient consensus criteria are respectively developed by proposing non-switched/switched distributed adaptive neural network-based dynamic event-trigger control schemes. At the end of this paper, some numerical simulations and comparison results are presented to imply the effectiveness of the proposed control strategies.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117492"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387000","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}
In this paper, we study the steepest descent method for unconstrained optimization problems involving quasiconvex fuzzy objective functions under granular differentiability. We introduce a class of granular quasiconvex and pseudoconvex functions, referred to as gr-quasiconvexity and gr-pseudoconvexity. Key properties of these functions and their interrelations are discussed. Leveraging the theory of quasi-Fejr convergence, we prove that the sequence generated by the steepest descent method with a generalized Armijo search converges completely to a granular stationary point of the fuzzy optimization problem. Several numerical examples are provided to demonstrate the effectiveness of the proposed approach. Additionally, a potential application in finance is considered and solved using our method.
{"title":"Steepest descent method with a generalized Armijo search to solve quasiconvex fuzzy optimization problems under granular differentiability","authors":"Shenglan Chen , Li Zhong , Zengbao Wu , Changjie Fang","doi":"10.1016/j.cam.2026.117432","DOIUrl":"10.1016/j.cam.2026.117432","url":null,"abstract":"<div><div>In this paper, we study the steepest descent method for unconstrained optimization problems involving quasiconvex fuzzy objective functions under granular differentiability. We introduce a class of granular quasiconvex and pseudoconvex functions, referred to as <em>gr</em>-quasiconvexity and <em>gr</em>-pseudoconvexity. Key properties of these functions and their interrelations are discussed. Leveraging the theory of quasi-Fej<span><math><mover><mi>e</mi><mo>´</mo></mover></math></span>r convergence, we prove that the sequence generated by the steepest descent method with a generalized Armijo search converges completely to a granular stationary point of the fuzzy optimization problem. Several numerical examples are provided to demonstrate the effectiveness of the proposed approach. Additionally, a potential application in finance is considered and solved using our method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117432"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387186","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}
Pub Date : 2026-10-01Epub Date: 2026-02-17DOI: 10.1016/j.cam.2026.117448
Qiumei Huang , Cheng Wang , Gangfan Zhong
In this paper, we propose two multi-step, linearized numerical schemes for a nonlinear convection-diffusion-reaction (CDR) equation with vanishing delay, a temporally nonlocal partial differential equation. These semi-implicit numerical schemes use a combination of explicit Adams–Bashforth extrapolation for the nonlinear term and implicit Adams–Moulton interpolation for the diffusion term. A long stencil finite difference approximation is employed for the spatial discretization, and a boundary extrapolation is used to prescribe the solution at “ghost” points lying outside of the computational domain. The numerical stability and convergence analysis is provided, and the discrete ℓ2 convergence estimate is obtained, with fourth-order spatial accuracy and high-order (third- or fourth-order) temporal accuracy. A few numerical experiments are also presented to confirm the theoretical results.
{"title":"Extended multi-step high-order numerical methods for the nonlinear convection-diffusion-reaction equation with vanishing delay","authors":"Qiumei Huang , Cheng Wang , Gangfan Zhong","doi":"10.1016/j.cam.2026.117448","DOIUrl":"10.1016/j.cam.2026.117448","url":null,"abstract":"<div><div>In this paper, we propose two multi-step, linearized numerical schemes for a nonlinear convection-diffusion-reaction (CDR) equation with vanishing delay, a temporally nonlocal partial differential equation. These semi-implicit numerical schemes use a combination of explicit Adams–Bashforth extrapolation for the nonlinear term and implicit Adams–Moulton interpolation for the diffusion term. A long stencil finite difference approximation is employed for the spatial discretization, and a boundary extrapolation is used to prescribe the solution at “ghost” points lying outside of the computational domain. The numerical stability and convergence analysis is provided, and the discrete ℓ<sup>2</sup> convergence estimate is obtained, with fourth-order spatial accuracy and high-order (third- or fourth-order) temporal accuracy. A few numerical experiments are also presented to confirm the theoretical results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117448"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387187","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}
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