Journal of Computational and Applied Mathematics最新文献

{"title":"An adaptive stochastic gradient method with variance reduction for smooth optimization problems","authors":"Mahmoud M. Yahaya ,&nbsp;Poom Kumam ,&nbsp;Thidaporn Seangwattana","doi":"10.1016/j.cam.2026.117559","DOIUrl":"10.1016/j.cam.2026.117559","url":null,"abstract":"<div><div>A Stochastic Gradient Descent(SGD) method has received more attention due to its efficient usage in machine learning. However, this method has some substantial defects, such as the high variance of the stochastic gradients and difficulty in selecting a practically performant learning rate. The former has been mitigated via the introduction of variance-reduced(VR) methods. These approaches reduce the noise due to variance in stochastic gradients; thus improving the convergence of the SGDs. However, these variants with VR property still inherit the latter knotty issue of SGD, where most adopted schemes resort to manual tuning of learning rate in practice. On the otherhand, other improvements with adaptive learning are established under some strong assumptions that may potentially limit their scope of usage. Consequently, this paper introduces a novel adaptive learning rate strategy into a minibatch variant of VR approach named StochaAstic Recursive grAdient algoritHm (SARAH), leading to SARAH-AD. The SARAH-AD algorithm enables an effective, efficient, robust, and automated computation of a suitable learning rate that is independent of the Lipchitz constant of the objective function. Moreover, the theoretical convergence analysis of SARAH-AD is extensively analyzed under a non-strong convexity case satisfying error-bound property. Furthermore, we analyzed the SARAH-AD in a general non-convex setting by requiring only an average <em>L</em>-smoothness, which is weaker than the usual <em>L</em>-smoothness assumption and also without bounded variance assumption. Moreover, we experimentally tested the performance of SARAH-AD on several medium to large-scale real-world datasets. The comparison uses convex and non-convex models with best-tuned algorithms. The proposed algorithm showed consistently better performance than other compared algorithms.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117559"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386899","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":"Joint deep calibration of the 4-factor PDV model","authors":"Fabio Baschetti ,&nbsp;Giacomo Bormetti ,&nbsp;Pietro Rossi","doi":"10.1016/j.cam.2026.117475","DOIUrl":"10.1016/j.cam.2026.117475","url":null,"abstract":"<div><div>Joint calibration to SPX and VIX market data is a delicate task that requires sophisticated modeling and incurs high computational costs. The latter is especially true when the pricing of volatility derivatives hinges on nested Monte Carlo simulation. One such example is the 4-factor Markov Path-Dependent Volatility (PDV) model of [1]. Nonetheless, its realism has earned it considerable attention in recent years. Gazzani and Guyon [2] marked a relevant contribution by learning the VIX as a random variable, i.e., a measurable function of the model parameters and the Markovian factors. A neural network replaces the inner simulation, making the joint calibration problem accessible. However, the minimization loop remains slow due to the expensive outer simulation. The present paper overcomes this limitation by learning SPX implied volatilities, VIX futures, and VIX call option prices. The pricing functions reduce to simple matrix-vector products that can be evaluated on the fly, shrinking calibration times to just a few seconds. Notably, we provide standard errors for the optimal calibration parameters.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117475"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386900","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":"A new 8-point binary interpolatory subdivision scheme with shape parameter and its applications","authors":"Abdul Ghaffar ,&nbsp;Muhammad Anwar ,&nbsp;Abdul Wasim Shaikh ,&nbsp;Pakeeza Ashraf ,&nbsp;Mustafa Inc ,&nbsp;Ali Akgül","doi":"10.1016/j.cam.2026.117532","DOIUrl":"10.1016/j.cam.2026.117532","url":null,"abstract":"<div><div>This paper introduces a new technique for the construction of an 8-point subdivision scheme (SS) with a shape parameter <em>μ</em>. Some well-known SSs are particular cases of our proposed 8-point binary SS. We find the parametric range in which the proposed SS generates <em>C</em>¹-continuous limit curves. It is observed that our proposed SS is <em>C</em>³-continuous for <span><math><mrow><mi>μ</mi><mo>=</mo><mfrac><mn>5</mn><mn>2048</mn></mfrac></mrow></math></span>. Some important properties of the proposed SS like the symmetry of basic limit function, exactness, approximation order, and convexity preservation are discussed. We also discuss error bounds and curvature of the limit curves of the proposed SS. Further, we illustrate the effectiveness of the shape parameter of the proposed SS through various applications of the SS. It is noted that the proposed SS has the potential to generate fractal curves for suitable choices of the shape parameter.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117532"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386994","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":"A new ADI framework for oil option pricing with cubic B-spline and Gauss-Hermite integration","authors":"Fares Alazemi,&nbsp;Abdulaziz Alsenafi","doi":"10.1016/j.cam.2026.117439","DOIUrl":"10.1016/j.cam.2026.117439","url":null,"abstract":"<div><div>This paper investigates the pricing of European options within the commodity market, specifically focusing on the dynamics of oil spot prices. We employ a long memory stochastic volatility model to effectively capture and predict the behavior of oil prices. Initially, we utilize statistical tests such as the Augmented Dickey-Fuller (ADF) test and other relevant techniques to extract essential characteristics from oil spot price data, thereby establishing a foundation for our analysis. To model these features, we propose a two-factor financial model grounded in a mixed fractional Brownian motion process. This approach is crucial, as it recognizes that the increments of the process exhibit dependence and retain long memory characteristics for values of <em>H</em> within the range <span><math><mrow><mo>(</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span>. However, this complexity poses challenges in deriving an explicit formula for forward contract pricing in commodity markets due to the inherent non-normal behavior of the underlying asset. To address this issue, we implement an advanced Monte Carlo method to approximate the prices of the contracts. This approach enables us to simulate a large number of potential price paths for oil, thereby facilitating more accurate pricing under the observed stochastic volatility conditions. Additionally, we incorporate stochastic calculus techniques alongside a delta hedging strategy to derive the partial differential equation (PDE) governing the option price. To solve this equation, we employ the Alternating Direction Implicit (ADI) method, known for its efficiency and stability in managing high-dimensional problems. Unlike explicit methods, which can suffer from stability issues and require very small time steps, the ADI method allows for larger time steps while maintaining stability, making it computationally efficient. This is particularly important in option pricing, where the financial markets can exhibit rapid changes. By leveraging these methodologies, the project aims to enhance the understanding of option pricing dynamics in the commodity market, providing valuable insights for traders and financial analysts involved in oil market operations.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117439"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387181","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":"Solvability of fractional integral equations by a family of measures of noncompactness in Fréchet algebra C(R+,C(J))","authors":"Hojjatollah Amiri Kayvanloo ,&nbsp;Hamid Mehravaran ,&nbsp;Ekrem Savaş ,&nbsp;Mohammad Mursaleen","doi":"10.1016/j.cam.2026.117425","DOIUrl":"10.1016/j.cam.2026.117425","url":null,"abstract":"<div><div>We define the Fr<span><math><mover><mi>e</mi><mo>´</mo></mover></math></span>chet algebra <span><math><mrow><mi>C</mi><mo>(</mo><msub><mi>R</mi><mo>+</mo></msub><mo>,</mo><mi>C</mi><mrow><mo>(</mo><mi>J</mi><mo>)</mo></mrow><mo>)</mo></mrow></math></span> and we introduce a new family of measures of noncompactness and a fixed point theorem that generalizes the Darbo’s fixed point theorem in this space. By applying the technique of measures of noncompactness and new fixed point theorem, we investigate the existence of solutions of a nonlinear fractional integral equations. Some examples are provided to support our main results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117425"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387126","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":"New continuous bivariate distributions developed based on general shock models","authors":"Hyunju Lee ,&nbsp;F.G. Badia ,&nbsp;Ji Hwan Cha","doi":"10.1016/j.cam.2026.117437","DOIUrl":"10.1016/j.cam.2026.117437","url":null,"abstract":"<div><div>In this study, we develop novel classes of continuous bivariate distributions based on general shock models. One class is that of absolutely continuous bivariate distributions, whereas the other one is that of non-absolutely continuous bivariate distributions. These classes are versatile in the sense that they can generate numerous families of distributions. We explore the distributional characteristics of the proposed classes, examining the bivariate ageing property and the dependence structure. Under some conditions, the proposed class of distributions satisfy certain kind of dependence property, called conditional PQD. Our result also reveals that a well-defined subclass of the proposed class satisfies the bivariate lack of memory property. Finally, we generate particular distribution families and apply them to two real-world datasets to illustrate their usefulness.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117437"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387127","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":"The modified Landweber iterative regularization method for a non-characteristic Cauchy problem in multiple dimensions","authors":"Jingjing Han ,&nbsp;Xiangtuan Xiong ,&nbsp;Yu Shen","doi":"10.1016/j.cam.2026.117460","DOIUrl":"10.1016/j.cam.2026.117460","url":null,"abstract":"<div><div>In this paper, we apply the modified Landweber iterative regularization method, including the classical Landweber iteration regularization method, to obtain the regularization solution of the non-characteristic Cauchy problem. It is well known that the problem is a seriously ill-posed problem, i.e. the solution (if it exists) does not depend continuously on the data. And then we give the corresponding error estimations, with an a-priori bound, under the a-priori and the a-posteriori regularization parameter selection rules, respectively. Finally, we verify the effectiveness of the method through a simple example.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117460"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147387132","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 volumes for the Gross-Pitaevskii equation","authors":"Quentin Chauleur","doi":"10.1016/j.cam.2026.117546","DOIUrl":"10.1016/j.cam.2026.117546","url":null,"abstract":"<div><div>We study the approximation by a semi-discrete finite-volume scheme of the Gross-Pitaevskii equation with time-dependent potential in two dimensions, performing a two-point flux approximation scheme in space. We rigorously analyze the error bounds relying on discrete uniform Sobolev inequalities. We finally perform some numerical simulations to investigate convergence error.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117546"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386634","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":"Novel two-level inertial algorithm for solving hierarchical equilibrium problem","authors":"Victor A. Uzor ,&nbsp;Oluwatosin T. Mewomo","doi":"10.1016/j.cam.2026.117499","DOIUrl":"10.1016/j.cam.2026.117499","url":null,"abstract":"<div><div>In this paper, we introduce a novel two-level inertial algorithm (TLIA) for solving a two-level (hierarchical) equilibrium problem. Unlike conventional inertial-based methods, our proposed TLIA adopts a dual inertial technique that features both one-step and two-step inertia components in one algorithm. This innovative approach provides a more robust and computationally efficient strategy that extends and outperforms familiar methods in the literature. In addition, we apply our proposed TLI algorithm to solving a generalized equilibrium problem whose constraint is the fixed point of a nonlinear demmimetric mapping. We prove weak and strong convergence results of our proposed method while assuming the bifunction to be pseudomonotone and strongly-pseudomonotone, respectively. Furthermore, we perform numerical experiments to validate the computational advantage of our proposed algorithm in comparison with various existing methods in the literature.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117499"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386638","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":"Dynamic opposition learning enhanced attaining and refining knowledge-based optimization algorithm for application to engineering design problems","authors":"Megha Varshney ,&nbsp;Davut Izci ,&nbsp;Serdar Ekinci","doi":"10.1016/j.cam.2026.117493","DOIUrl":"10.1016/j.cam.2026.117493","url":null,"abstract":"<div><div>Achieving the right trade-off between exploration and exploitation is a critical hurdle in nature-inspired optimization algorithms, particularly when addressing complex, real-world global optimization problems. Maintaining this balance allows the algorithm's agents to efficiently investigate unexplored regions of the search space. The Attaining and Refining Knowledge-Based Optimization Algorithm (ARKO) is a recently developed metaheuristic that draws inspiration from human learning behavior, utilizing shared knowledge across the population to guide the search process. However, ARKO sometimes fails to locate the best solutions, getting trapped in suboptimal points, which results in early convergence and obstructs the discovery of global optima. To overcome these shortcomings, this research introduces an improved version called, DOL (Dynamic Opposition Learning) inspired Attaining-Refining Knowledge based Optimization (DARKO), aimed at enhancing the interplay between exploration and exploitation while avoiding local traps. The approach strengthens ARKO’s exploratory capacity by incorporating Dynamic Oppositional Learning (DOL) that ensures a harmonious balance between the two phases by using its dynamic search process. With its adaptable search domain and minimal computational overhead, the DOL-inspired ARKO mechanism boosts exploration efficiency and supports robust convergence toward superior solutions, effectively curbing premature convergence. The effectiveness of DARKO is assessed using the widely recognized IEEE CEC 2019 and IEEE CEC 2022 benchmark suites, complemented by three practical engineering applications. Comparative analysis with established metaheuristic methods, supported by quantitative data, demonstrates DARKO’s remarkable proficiency and optimization ability.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"484 ","pages":"Article 117493"},"PeriodicalIF":2.6,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386896","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}