Journal of Computational and Applied Mathematics最新文献

{"title":"Two hybrid conjugate gradient based algorithms on Riemannian manifolds with adaptive restart strategy for nonconvex optimization problems","authors":"Meixuan Jiang ,&nbsp;Yun Wang ,&nbsp;Hu Shao ,&nbsp;Ting Wu ,&nbsp;Weiwei Sun","doi":"10.1016/j.cam.2024.116452","DOIUrl":"10.1016/j.cam.2024.116452","url":null,"abstract":"<div><div>In this paper, we propose two hybrid conjugate gradient algorithms for solving nonconvex optimization problems on Riemannian manifolds. The conjugate parameter of the first method extends a hybrid formula [Comput. Oper. Res. 159 (2023) 106341] from Euclidean to Riemannian spaces. The conjugate parameter of the second method integrates the Fletcher–Reeves conjugate parameter with another flexible conjugate parameter. An adaptive restart strategy is then incorporated into their respective search directions to enhance their theoretical properties and computational efficiency. As a result, both methods independently generate sufficient descent directions regardless of any stepsize strategy on Riemannian manifolds. Under typical assumptions and using the Riemannian weak Wolfe conditions to generate stepsize, the global convergence results of these two families are demonstrated. Numerical comparisons with existing methods using different Riemannian optimization scenarios verify the effectiveness of our proposed methods.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116452"},"PeriodicalIF":2.1,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096362","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}

{"title":"Non-fragile sampled-data control for uncertain fractional-order systems with time-varying delay","authors":"Lianglin Xiong ,&nbsp;Junzhou Dai ,&nbsp;Haiyang Zhang","doi":"10.1016/j.cam.2024.116438","DOIUrl":"10.1016/j.cam.2024.116438","url":null,"abstract":"<div><div>The aim of this paper is to investigate a novel fractional order integral inequality (FOII) for reducing the conservatism of the stability and the non-fragile sampled-data control (NFSDC) criterion for the uncertain fractional-order systems (FOSs) with time-varying delay (TVD). Firstly, in order to estimate the quadratic derivative of fractional-order integral more accurately, a new FOII with free weighting matrix is proposed, which has a tighter upper bound than the existing FOII. Second, in order to more accurately reflect the delay variation and reduce the data transmission frequency, the influence of uncertainty and time-varying delay are considered, the NFSDC scheme followed by the discussed stability criterion is given based on our novel piecewise Lyapunov functional and introduced FOII. Finally, three numerical examples demonstrate the feasibility and superiority of the proposed method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116438"},"PeriodicalIF":2.1,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096360","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}

{"title":"Two explicit methods for one-sided Lipschitz stochastic differential equations driven by fractional Brownian motion","authors":"Jingjun Zhao,&nbsp;Hao Zhou,&nbsp;Yang Xu","doi":"10.1016/j.cam.2024.116462","DOIUrl":"10.1016/j.cam.2024.116462","url":null,"abstract":"<div><div>For solving the stochastic differential equations with the one-sided Lipschitz and polynomial increasing drift coefficients driven by fractional Brownian motion, we propose the tamed Euler–Maruyama method and the explicit Euler–Maruyama method with projection. By using the modified coefficients, the errors of these two explicit methods are analyzed recursively and the convergence rates are obtained. A numerical experiment is carried out to support our theoretical results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116462"},"PeriodicalIF":2.1,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096413","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}

{"title":"Finite time stability of neutral multiterm fractional order time-varying delay systems","authors":"K. Kaliraj ,&nbsp;P.K. Lakshmi Priya ,&nbsp;V. Tamilarasan ,&nbsp;S. Suresh","doi":"10.1016/j.cam.2024.116459","DOIUrl":"10.1016/j.cam.2024.116459","url":null,"abstract":"<div><div>In this paper, the finite-time stability of neutral multi-term fractional order system of non-linear type with time-varying input and state delays is investigated. Using the effectiveness of Banach fixed point theorem for generalized metric spaces, new sufficient conditions for finite-time stability of the considered system has been identified. Finally, numerical examples are given to get a better understanding of the theoretical results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116459"},"PeriodicalIF":2.1,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143092131","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}

{"title":"Reciprocal solution existence results for a class of vector variational control inequalities with application in physics","authors":"Savin Treanţă ,&nbsp;Vinay Singh ,&nbsp;Shashi Kant Mishra","doi":"10.1016/j.cam.2024.116461","DOIUrl":"10.1016/j.cam.2024.116461","url":null,"abstract":"<div><div>By considering differentiability and generalized convexity hypotheses for some functionals of multiple integral type, we propose some equivalences between the solution sets of some (weak) variational control inequalities of vector type, which depend by some uncertainty parameters, and the associated multiple objective variational control problems. Moreover, we propose the physical motivation of the problem under investigation by providing an application in the end of the paper.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116461"},"PeriodicalIF":2.1,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096235","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}

{"title":"On the solution of Dolichobrachistochrone differential game via dynamic programming approach","authors":"Aicha Ghanem ,&nbsp;Touffik Bouremani ,&nbsp;Djamel Benterki","doi":"10.1016/j.cam.2024.116460","DOIUrl":"10.1016/j.cam.2024.116460","url":null,"abstract":"<div><div>This study aims to apply Mirică’s new dynamic programming method, introduced in 2004, to derive the rigorous solution of the famous Dolichobrachistochrone differential game, originally proposed by Isaacs in 1965. In addition, it aims to identify, for the first time, feedback strategies, a novel contribution that offers significant advantages in game theory over other types of strategies. Among them, they promote efficiency through dynamic performance optimization, leading to improved resource utilization and goal attainment. Moreover, their simplicity facilitates implementation and analysis, reducing computational complexity. The essential tool in our approach, involves the use of a certain refinement of Cauchy’s method of characteristics for stratified Hamilton–Jacobi equations, to describe a large class of admissible trajectories and to identify a domain in which the value function exists. As a rigorous criterion for proving the optimality of these admissible feedback strategies, we use the well-known verification Theorem for locally Lipschitz value functions as a sufficient optimality condition.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116460"},"PeriodicalIF":2.1,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096364","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}

{"title":"Generalized exponential time differencing for fractional oscillation models","authors":"Aljowhara H. Honain ,&nbsp;Khaled M. Furati ,&nbsp;Ibrahim O. Sarumi ,&nbsp;Abdul Q.M. Khaliq","doi":"10.1016/j.cam.2024.116456","DOIUrl":"10.1016/j.cam.2024.116456","url":null,"abstract":"<div><div>Oscillations occur in various processes and are of great significance for understanding, analyzing and simulating real-world phenomena. Fractional evolution equations of oscillatory type provide an effective tool to model some anomalous oscillatory behaviors. Generally, solutions of these equations exhibit oscillatory behavior which can sometimes be erratic. Therefore, developing efficient numerical methods that adequately capture the oscillatory behavior of these solutions can be challenging. In this paper, an efficient novel second-order numerical scheme is developed for a class of fractional oscillation models. The scheme is based on the exponential time differencing technique, special approximations of Mittag-Leffler function, and the non-uniform mesh. Convergence and the stability analysis are conducted and verified through numerical experiments. In particular, we illustrate the potential of the numerical scheme as a time integrator for fractional diffusion-wave equations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116456"},"PeriodicalIF":2.1,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143135613","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}

{"title":"Hemispheroidal parameterization and harmonic decomposition of simply connected open surfaces","authors":"Gary P.T. Choi ,&nbsp;Mahmoud Shaqfa","doi":"10.1016/j.cam.2024.116455","DOIUrl":"10.1016/j.cam.2024.116455","url":null,"abstract":"<div><div>Spectral analysis of open surfaces is gaining momentum for studying surface morphology in engineering, computer graphics, and medical domains. This analysis is enabled using proper parameterization approaches on the target analysis domain. In this paper, we propose the usage of customizable parameterization coordinates that allow mapping open surfaces into oblate or prolate hemispheroidal surfaces. For this, we proposed the usage of Tutte, conformal, area-preserving, and balanced mappings for parameterizing any given simply connected open surface onto an optimal hemispheroid. The hemispheroidal harmonic bases were introduced to spectrally expand open parametric surfaces by generalizing the known hemispherical ones. This approach uses the depth of the hemispheroid as a degree of freedom to control the size of the parameterization domain of the open surfaces while providing numerically stable basis functions. Several open surfaces have been tested using different mapping combinations. We also propose optimization-based mappings to serve various applications on the reconstruction problem. Altogether, our work provides an effective way to represent and analyze simply connected open surfaces.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116455"},"PeriodicalIF":2.1,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096363","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}

{"title":"Outlier detection of multivariate data via the maximization of the cumulant generating function","authors":"Francesco Cesarone ,&nbsp;Rosella Giacometti ,&nbsp;Jacopo Maria Ricci","doi":"10.1016/j.cam.2024.116457","DOIUrl":"10.1016/j.cam.2024.116457","url":null,"abstract":"<div><div>In this paper, we propose an outlier detection algorithm for multivariate data based on their projections on the directions that maximize the Cumulant Generating Function (CGF). We prove that CGF is a convex function, and we characterize the CGF maximization problem on the unit <span><math><mi>n</mi></math></span>-circle as a concave minimization problem. Then, we show that the CGF maximization approach can be interpreted as an extension of the standard principal component technique. Therefore, for validation and testing, we provide a thorough comparison of our methodology with two other projection-based approaches both on artificial and real-world financial data. Finally, we apply our method as an early detector for financial crises.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116457"},"PeriodicalIF":2.1,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasi-Monte Carlo integration over Rs based on digital nets","authors":"Josef Dick ,&nbsp;Friedrich Pillichshammer","doi":"10.1016/j.cam.2024.116451","DOIUrl":"10.1016/j.cam.2024.116451","url":null,"abstract":"<div><div>This paper discusses <span><math><mi>φ</mi></math></span>-weighted integration of functions over the <span><math><mi>s</mi></math></span>-dimensional Euclidean space using quasi-Monte Carlo (QMC) rules combined with an inversion method, where the probability density function (PDF) <span><math><mi>φ</mi></math></span> is of product form, i.e., a product of uni-variate PDFs <span><math><msub><mrow><mi>φ</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> for each coordinate <span><math><mi>i</mi></math></span> in <span><math><mrow><mo>{</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>s</mi><mo>}</mo></mrow></math></span>.</div><div>The space of integrands is specified by means of a <span><math><mi>γ</mi></math></span>-weighted <span><math><mi>p</mi></math></span>-norm, <span><math><mrow><mi>p</mi><mo>≥</mo><mn>1</mn></mrow></math></span>, which involves coordinate weights <span><math><mi>γ</mi></math></span>, the partial derivatives of order up to one of the integrands as well as additional weight functions <span><math><msub><mrow><mi>ψ</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> and the PDFs <span><math><msub><mrow><mi>φ</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>. The coordinate weights <span><math><mi>γ</mi></math></span> model the importance of different coordinates or groups of coordinates in the sense of Sloan and Woźniakowski, and the weight functions <span><math><msub><mrow><mi>ψ</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> are additional parameters of the space which describe the decay of the partial derivatives of the integrands. Fast decaying weights <span><math><mrow><msub><mrow><mi>ψ</mi></mrow><mrow><mi>i</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> for <span><math><mrow><mi>x</mi><mo>→</mo><mo>±</mo><mi>∞</mi></mrow></math></span> enlarge the space of functions with finite norm, but decrease the convergence rate of the worst-case error of the proposed algorithms.</div><div>Our algorithms for integration use digitally shifted digital nets in combination with an inversion method. We study the (root) mean squared worst-case error with respect to random digital shifts. The obtained error bounds depend on the choice of weight functions <span><math><msub><mrow><mi>ψ</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> and coordinate weights <span><math><mi>γ</mi></math></span>. Under certain conditions on <span><math><mi>γ</mi></math></span>, these bounds hold uniformly for all dimensions <span><math><mi>s</mi></math></span>.</div><div>Numerical experiments demonstrate the effectiveness of the proposed algorithms.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"462 ","pages":"Article 116451"},"PeriodicalIF":2.1,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143145552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}