Computational and Applied Mathematics最新文献_第8页

Identification methods for ordinal potential differential games 序数势差博弈的识别方法

IF 2.6 3区数学

Computational and Applied Mathematics Pub Date : 2024-07-26 DOI: 10.1007/s40314-024-02861-w

Balint Varga, Da Huang, Sören Hohmann

{"title":"Identification methods for ordinal potential differential games","authors":"Balint Varga, Da Huang, Sören Hohmann","doi":"10.1007/s40314-024-02861-w","DOIUrl":"https://doi.org/10.1007/s40314-024-02861-w","url":null,"abstract":"This paper introduces two new identification methods for linear quadratic (LQ) ordinal potential differential games (OPDGs). Potential games are notable for their benefits, such as the computability and guaranteed existence of Nash Equilibria. While previous research has analyzed ordinal potential static games, their applicability to various engineering applications remains limited. Despite the earlier introduction of OPDGs, a systematic method for identifying a potential game for a given LQ differential game has not yet been developed. To address this gap, we propose two identification methods to provide the quadratic potential cost function for a given LQ differential game. Both methods are based on linear matrix inequalities (LMIs). The first method aims to minimize the condition number of the potential cost function’s parameters, offering a faster and more precise technique compared to earlier solutions. In addition, we present an evaluation of the feasibility of the structural requirements of the system. The second method, with a less rigid formulation, can identify LQ OPDGs in cases where the first method fails. These novel identification methods are verified through simulations, demonstrating their advantages and potential in designing and analyzing cooperative control systems.","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"16 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141771037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 primal-dual active set approach to the valuation of American options in regime-switching models: numerical solutions and convergence analysis 制度转换模型中美式期权估值的原始二元有源集方法：数值解与收敛分析

IF 2.6 3区数学

Computational and Applied Mathematics Pub Date : 2024-07-26 DOI: 10.1007/s40314-024-02862-9

Xin Wen, Haiming Song, Yutian Li, Zihan Gao

{"title":"A primal-dual active set approach to the valuation of American options in regime-switching models: numerical solutions and convergence analysis","authors":"Xin Wen, Haiming Song, Yutian Li, Zihan Gao","doi":"10.1007/s40314-024-02862-9","DOIUrl":"https://doi.org/10.1007/s40314-024-02862-9","url":null,"abstract":"In this study, we explore the valuation challenge posed by American options subject to regime switching, utilizing a model defined by a complex system of parabolic variational inequalities within an infinite domain. The initial pricing model is transformed into a linear complementarity problem (LCP) in a bounded rectangular domain, achieved through the application of a priori estimations and the introduction of an appropriate artificial boundary condition. To discretize the LCP, we employ a finite difference method (FDM), and address the resulting discretized system using a primal-dual active set (PDAS) strategy. The PDAS approach is particularly advantageous for its ability to concurrently determine the option’s price and the optimal exercise boundary. This paper conducts an extensive convergence analysis, evaluating both the truncation error associated with the FDM and the iteration error of the PDAS. Comprehensive numerical simulations are performed to validate the method’s accuracy and efficiency, underscoring its significant potential for application in the field of financial mathematics.","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"63 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

The $$gamma $$ -diagonally dominant degree of Schur complements and its applications 舒尔互补的对角主导度及其应用

IF 2.6 3区数学

Computational and Applied Mathematics Pub Date : 2024-07-24 DOI: 10.1007/s40314-024-02868-3

Zhenhua Lyu, Lixin Zhou, Junye Ma

引用次数: 0

Discontinuous harvesting policy in a Filippov system involving prey refuge 涉及猎物避难所的菲利波夫系统中的不连续收获政策

IF 2.6 3区数学

Computational and Applied Mathematics Pub Date : 2024-07-23 DOI: 10.1007/s40314-024-02858-5

Rajesh Ranjan Patra, Sarit Maitra

引用次数: 0

On some geometrical eigenvalue inverse problems involving the p-Laplacian operator 关于涉及 p 拉普拉斯算子的一些几何特征值逆问题

IF 2.6 3区数学

Computational and Applied Mathematics Pub Date : 2024-07-23 DOI: 10.1007/s40314-024-02855-8

Abdelkrim Chakib, Ibrahim Khalil

{"title":"On some geometrical eigenvalue inverse problems involving the p-Laplacian operator","authors":"Abdelkrim Chakib, Ibrahim Khalil","doi":"10.1007/s40314-024-02855-8","DOIUrl":"https://doi.org/10.1007/s40314-024-02855-8","url":null,"abstract":"In this paper, we deal with some shape optimization geometrical inverse spectral problems involving the first eigenvalue and eigenfunction of a p-Laplace operator, over a class of open domains with prescribed volume. We first briefly show the existence of the optimal shape design for the (L^p) norm of the eigenfunctions. We carried out the shape derivative calculation of this shape optimization problem using deformation of domains by vector fields. Then we propose a numerical method using lagrangian functional, Hadamard’s shape derivative and gradient method to determine the minimizers for this shape optimization problem. We investigate also numerically the problem of minimizing the first eigenvalue of the p-Laplacian-Dirichlet operator with volume-constraint on domains, using constrained and unconstrained shape optimization formulations. The resulting proposed algorithms of the optimization process are based on the inverse power algorithm (Biezuner et al. 2012) and the finite elements method performed to approximate the first eigenvalue and related eigenfunction. Numerical examples and illustrations are provided for different constrained and unconstrained shape optimization formulations and for various cost functionals to show the efficiency and practical suitability of the proposed approach.","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"39 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141771043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Accurate approximations of classical and generalized binomial coefficients 经典二项式系数和广义二项式系数的精确近似值

IF 2.6 3区数学

Computational and Applied Mathematics Pub Date : 2024-07-23 DOI: 10.1007/s40314-024-02851-y

Vito Lampret

引用次数: 0

Modified two-step modulus-based matrix splitting iteration methods for implicit complementarity problems 隐式互补问题的基于模数的修正两步矩阵分割迭代法

IF 2.6 3区数学

Computational and Applied Mathematics Pub Date : 2024-07-22 DOI: 10.1007/s40314-024-02860-x

Lu-Xin Wang, Yang Cao, Qin-Qin Shen, Chen-Can Zhou

引用次数: 0

Piecewise Jacobi–Gauss spectral collocation simulations for a multi-particle model involving processing delay 涉及处理延迟的多粒子模型的分段雅各比-高斯谱配准模拟

IF 2.6 3区数学

Computational and Applied Mathematics Pub Date : 2024-07-22 DOI: 10.1007/s40314-024-02843-y

Quan Zhou, Yinkun Wang, Lingling Ma, Yicheng Liu

引用次数: 0

On regular triangle-distinct graphs 关于正三角形区分图

IF 2.6 3区数学

Computational and Applied Mathematics Pub Date : 2024-07-19 DOI: 10.1007/s40314-024-02854-9

Dragan Stevanović, Mohammad Ghebleh, Gilles Caporossi, Ambat Vijayakumar, Sanja Stevanović

引用次数: 0

A new approach to soft relations and soft functions 软关系和软函数的新方法

IF 2.6 3区数学

Computational and Applied Mathematics Pub Date : 2024-07-18 DOI: 10.1007/s40314-024-02853-w

Adem Yolcu, Taha Yasin Ozturk, Sadi Bayramov

引用次数: 0