Pub Date : 2024-12-24DOI: 10.1016/j.cam.2024.116449
Jinran Yao, Zhengwei Yin
This work investigates the mean-square contractivity of two types of split-step backward Milstein schemes for commutative stochastic differential equations (SDEs) with non-globally Lipschitz continuous coefficients. Our setting allows the drift coefficient to satisfy a one-sided Lipschitz condition and the diffusion coefficient to satisfy a global Lipschitz condition, thereby including well-known examples such as the stochastic Ginzburg–Landau equation and the stochastic Verhulst equation. Our results demonstrate that both of the numerical schemes considered can accurately reproduce the mean-square contractivity of the nonlinear SDEs mentioned. Finally, some numerical experiments are performed to illustrate the validity of the theoretical results.
{"title":"Numerical contractivity of split-step backward Milstein-type schemes for commutative SDEs with non-globally Lipschitz continuous coefficients","authors":"Jinran Yao, Zhengwei Yin","doi":"10.1016/j.cam.2024.116449","DOIUrl":"10.1016/j.cam.2024.116449","url":null,"abstract":"<div><div>This work investigates the mean-square contractivity of two types of split-step backward Milstein schemes for commutative stochastic differential equations (SDEs) with non-globally Lipschitz continuous coefficients. Our setting allows the drift coefficient to satisfy a one-sided Lipschitz condition and the diffusion coefficient to satisfy a global Lipschitz condition, thereby including well-known examples such as the stochastic Ginzburg–Landau equation and the stochastic Verhulst equation. Our results demonstrate that both of the numerical schemes considered can accurately reproduce the mean-square contractivity of the nonlinear SDEs mentioned. Finally, some numerical experiments are performed to illustrate the validity of the theoretical results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116449"},"PeriodicalIF":2.1,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096237","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 : 2024-12-24DOI: 10.1016/j.cam.2024.116453
Yingxiao Wang , Lingchen Kong , Houduo Qi
Portfolio selection has always been a widely concerned issue in optimization and investment. Due to various forms of market friction, such as transaction costs and management fees, investors must choose a small number of assets from an asset pool. It naturally leads to the portfolio model with cardinality constraint. However, it is hard to solve this model accurately. Researchers generally use approximate methods to solve it, such as norm penalty. Unfortunately, these methods may not guarantee that the cardinality constraint is consistently met. In addition, short positions are challenging to implement in practice and are forbidden in some markets. Therefore, in this paper, we consider the long-only global minimum variance portfolio with cardinality constraint. We study the nonnegative cardinality constraint directly: defining the strong -Lagrangian stationary point by nonnegative sparse projection operator, establishing the first-order optimality conditions in terms of the Lagrangian stationary point, as well as developing the Lagrange Newton algorithm to significantly reduce the scale of our problem and solve it directly. Finally, we conduct extensive experiments on real data sets. The numerical results show that the out-of-sample performances of our portfolio are better than some commonly used portfolio models for most data sets. Our portfolios usually lead to a higher Sharpe ratio and lower transaction costs with investment in fewer assets.
{"title":"An efficient Lagrange–Newton algorithm for long-only cardinality constrained portfolio selection on real data sets","authors":"Yingxiao Wang , Lingchen Kong , Houduo Qi","doi":"10.1016/j.cam.2024.116453","DOIUrl":"10.1016/j.cam.2024.116453","url":null,"abstract":"<div><div>Portfolio selection has always been a widely concerned issue in optimization and investment. Due to various forms of market friction, such as transaction costs and management fees, investors must choose a small number of assets from an asset pool. It naturally leads to the portfolio model with cardinality constraint. However, it is hard to solve this model accurately. Researchers generally use approximate methods to solve it, such as <span><math><msub><mrow><mi>l</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> norm penalty. Unfortunately, these methods may not guarantee that the cardinality constraint is consistently met. In addition, short positions are challenging to implement in practice and are forbidden in some markets. Therefore, in this paper, we consider the long-only global minimum variance portfolio with cardinality constraint. We study the nonnegative cardinality constraint directly: defining the strong <span><math><mi>β</mi></math></span>-Lagrangian stationary point by nonnegative sparse projection operator, establishing the first-order optimality conditions in terms of the Lagrangian stationary point, as well as developing the Lagrange Newton algorithm to significantly reduce the scale of our problem and solve it directly. Finally, we conduct extensive experiments on real data sets. The numerical results show that the out-of-sample performances of our portfolio are better than some commonly used portfolio models for most data sets. Our portfolios usually lead to a higher Sharpe ratio and lower transaction costs with investment in fewer assets.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116453"},"PeriodicalIF":2.1,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096233","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 : 2024-12-20DOI: 10.1016/j.cam.2024.116443
Ignacio Labarca-Figueroa , Ralf Hiptmair
We study frequency domain electromagnetic scattering at a bounded, penetrable, and inhomogeneous obstacle . From the Stratton-Chu integral representation, we derive a new representation formula when constant reference coefficients are given for the interior domain. The resulting integral representation contains the usual layer potentials, but also volume potentials on . Then it is possible to follow a single-trace approach to obtain boundary integral equations perturbed by traces of compact volume integral operators with weakly singular kernels. The coupled boundary and volume integral equations are discretized with a Galerkin approach with usual Curl-conforming and Div-conforming finite elements on the boundary and in the volume. Compression techniques and special quadrature rules for singular integrands are required for an efficient and accurate method. Numerical experiments provide evidence that our new formulation enjoys promising properties.
{"title":"Coupled boundary and volume integral equations for electromagnetic scattering","authors":"Ignacio Labarca-Figueroa , Ralf Hiptmair","doi":"10.1016/j.cam.2024.116443","DOIUrl":"10.1016/j.cam.2024.116443","url":null,"abstract":"<div><div>We study frequency domain electromagnetic scattering at a bounded, penetrable, and inhomogeneous obstacle <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math></span>. From the Stratton-Chu integral representation, we derive a new representation formula when constant reference coefficients are given for the interior domain. The resulting integral representation contains the usual layer potentials, but also volume potentials on <span><math><mi>Ω</mi></math></span>. Then it is possible to follow a single-trace approach to obtain boundary integral equations perturbed by traces of compact volume integral operators with weakly singular kernels. The coupled boundary and volume integral equations are discretized with a Galerkin approach with usual Curl-conforming and Div-conforming finite elements on the boundary and in the volume. Compression techniques and special quadrature rules for singular integrands are required for an efficient and accurate method. Numerical experiments provide evidence that our new formulation enjoys promising properties.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116443"},"PeriodicalIF":2.1,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096263","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}
Pub Date : 2024-12-19DOI: 10.1016/j.cam.2024.116444
Zaizai Yan, Yanjie Shi, Xiuyun Peng
This paper examines the reliability of systems composed of components with multiple performances that degrade over time, resulting in competing failures between soft and hard failures. The flexible Tweedie Exponential Diffusion process is employed to model the performance degradation, while the dependence between multiple performances degradation processes is established by the Copula functions. Additionally, we utilize the Weibull distribution to characterize the failure times of hard failures and construct a proportional hazards model to relate the hard failure rate to performance degradation. To estimate the model parameters and reliability function, we apply a two-stage Bayesian approach, employing the efficient Hamiltonian Monte Carlo algorithm for parameter estimation. Through simulation studies, the proposed model and method have good statistical inference performance. Finally, the constructed model and method are implemented in real data to showcase its practical applicability.
{"title":"Reliability analysis of k/n(G) degradation system under dependent competing failures","authors":"Zaizai Yan, Yanjie Shi, Xiuyun Peng","doi":"10.1016/j.cam.2024.116444","DOIUrl":"10.1016/j.cam.2024.116444","url":null,"abstract":"<div><div>This paper examines the reliability of <span><math><mrow><mi>k</mi><mo>/</mo><mi>n</mi><mspace></mspace><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> systems composed of components with multiple performances that degrade over time, resulting in competing failures between soft and hard failures. The flexible Tweedie Exponential Diffusion process is employed to model the performance degradation, while the dependence between multiple performances degradation processes is established by the Copula functions. Additionally, we utilize the Weibull distribution to characterize the failure times of hard failures and construct a proportional hazards model to relate the hard failure rate to performance degradation. To estimate the model parameters and reliability function, we apply a two-stage Bayesian approach, employing the efficient Hamiltonian Monte Carlo algorithm for parameter estimation. Through simulation studies, the proposed model and method have good statistical inference performance. Finally, the constructed model and method are implemented in real data to showcase its practical applicability.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116444"},"PeriodicalIF":2.1,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096260","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 : 2024-12-19DOI: 10.1016/j.cam.2024.116450
Andreas Bartel , Manuel Schaller
Port-Hamiltonian systems provide an energy-based modeling paradigm for dynamical input-state-output systems. At their core, they fulfill an energy balance relating stored, dissipated and supplied energy. To accurately resolve this energy balance in time discretizations, we propose an adaptive grid refinement technique based on a posteriori error estimation. The evaluation of the error estimator includes the computation of adjoint sensitivities. To interpret this adjoint equation as a backwards-in-time equation, we show piecewise weak differentiability of the dual variable. Then, leveraging dissipativity of the port-Hamiltonian dynamics, we present a parallelizable approximation of the underlying adjoint system in the spirit of a block-Jacobi method to efficiently compute error indicators. We illustrate the performance of the proposed scheme by means of numerical experiments showing that it yields a smaller violation of the energy balance when compared to uniform refinements and traditional step size controlled time stepping.
{"title":"Goal-oriented time adaptivity for port-Hamiltonian systems","authors":"Andreas Bartel , Manuel Schaller","doi":"10.1016/j.cam.2024.116450","DOIUrl":"10.1016/j.cam.2024.116450","url":null,"abstract":"<div><div>Port-Hamiltonian systems provide an energy-based modeling paradigm for dynamical input-state-output systems. At their core, they fulfill an energy balance relating stored, dissipated and supplied energy. To accurately resolve this energy balance in time discretizations, we propose an adaptive grid refinement technique based on a posteriori error estimation. The evaluation of the error estimator includes the computation of adjoint sensitivities. To interpret this adjoint equation as a backwards-in-time equation, we show piecewise weak differentiability of the dual variable. Then, leveraging dissipativity of the port-Hamiltonian dynamics, we present a parallelizable approximation of the underlying adjoint system in the spirit of a block-Jacobi method to efficiently compute error indicators. We illustrate the performance of the proposed scheme by means of numerical experiments showing that it yields a smaller violation of the energy balance when compared to uniform refinements and traditional step size controlled time stepping.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116450"},"PeriodicalIF":2.1,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096262","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}
In this paper, we propose an identification algorithm that utilizes the least squares principle based on the auxiliary model for parameter identification of discrete time-delay periodic linear systems. Initially, we introduce the period transfer operator, which adopts an input–output representation to ascertain the response of periodic systems across periods. Building on this concept, we use the auxiliary model to replace the undetermined variables in the system. Subsequently, we present an auxiliary model recursive least squares identification algorithm to identify the parameters of time-delay discrete linear periodic systems. Finally, we provide two numerical examples to demonstrate the algorithm’s effectiveness in identifying discrete time-delay periodic linear systems.
{"title":"A recursive identification algorithm for discrete time-delay periodic linear systems","authors":"Lingling Lv , Jiali Zhao , Bingqian Zheng , Jianwei Shen , Huaicheng Yan","doi":"10.1016/j.cam.2024.116447","DOIUrl":"10.1016/j.cam.2024.116447","url":null,"abstract":"<div><div>In this paper, we propose an identification algorithm that utilizes the least squares principle based on the auxiliary model for parameter identification of discrete time-delay periodic linear systems. Initially, we introduce the period transfer operator, which adopts an input–output representation to ascertain the response of periodic systems across periods. Building on this concept, we use the auxiliary model to replace the undetermined variables in the system. Subsequently, we present an auxiliary model recursive least squares identification algorithm to identify the parameters of time-delay discrete linear periodic systems. Finally, we provide two numerical examples to demonstrate the algorithm’s effectiveness in identifying discrete time-delay periodic linear systems.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116447"},"PeriodicalIF":2.1,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096261","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 : 2024-12-16DOI: 10.1016/j.cam.2024.116441
Başak Bulut Karageyi̇k
This paper investigates the problem of optimal reinsurance by evaluating four critical criteria: ruin probability, variance of retained risk, profit, and expected utility. The study focuses on proportional-XL reinsurance, which combines the benefits of both proportional and excess of loss (XL) reinsurance.
Using a classical risk model with a compound Poisson process for aggregate claims, the paper demonstrates that De Vylder’s approximation effectively estimates the ruin probability from the perspectives of both the insurer and the reinsurer, incorporating a two-dimensional risk process. The impact of reinsurance levels on each criterion is analyzed separately for the insurer and the reinsurer, providing a comprehensive understanding of reinsurance effects.
The optimal reinsurance level is determined by balancing conflicting objectives: maximizing profit and expected utility while minimizing ruin probability and variance. Multiple-criteria decision-making (MCDM) techniques, specifically the COPRAS and COPRAS-G methods, are applied to tailor optimal reinsurance strategies for both parties.
A detailed application of these methods for exponential and Pareto claim distributions enables a comparison based on the portfolio’s tail behavior. The cost-effectiveness of reinsurance agreements is evaluated, showing that reinsurance is more cost-effective than no reinsurance in both models. As expected, the cost-effectiveness of the proposed methods varies depending on the characteristics of the exponential and Pareto distributions.
{"title":"An integrated framework for indicator-based decision analysis in proportional-XL reinsurance","authors":"Başak Bulut Karageyi̇k","doi":"10.1016/j.cam.2024.116441","DOIUrl":"10.1016/j.cam.2024.116441","url":null,"abstract":"<div><div>This paper investigates the problem of optimal reinsurance by evaluating four critical criteria: ruin probability, variance of retained risk, profit, and expected utility. The study focuses on proportional-XL reinsurance, which combines the benefits of both proportional and excess of loss (XL) reinsurance.</div><div>Using a classical risk model with a compound Poisson process for aggregate claims, the paper demonstrates that De Vylder’s approximation effectively estimates the ruin probability from the perspectives of both the insurer and the reinsurer, incorporating a two-dimensional risk process. The impact of reinsurance levels on each criterion is analyzed separately for the insurer and the reinsurer, providing a comprehensive understanding of reinsurance effects.</div><div>The optimal reinsurance level is determined by balancing conflicting objectives: maximizing profit and expected utility while minimizing ruin probability and variance. Multiple-criteria decision-making (MCDM) techniques, specifically the COPRAS and COPRAS-G methods, are applied to tailor optimal reinsurance strategies for both parties.</div><div>A detailed application of these methods for exponential and Pareto claim distributions enables a comparison based on the portfolio’s tail behavior. The cost-effectiveness of reinsurance agreements is evaluated, showing that reinsurance is more cost-effective than no reinsurance in both models. As expected, the cost-effectiveness of the proposed methods varies depending on the characteristics of the exponential and Pareto distributions.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116441"},"PeriodicalIF":2.1,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096232","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 : 2024-12-14DOI: 10.1016/j.cam.2024.116442
Bo Li, Qinglong Gao
Portfolio optimization is an important class of decision management problems. In addition, data envelopment analysis method is often used to evaluate the pros and cons of the portfolio. In this paper, we propose a bi-objective portfolio model based on uncertainty theory, and present an uncertain Banker–Charnes–Cooper-data envelopment analysis (BCC-DEA) model to evaluate uncertain portfolios of risky assets. Firstly, we propose an uncertain bi-objective portfolio model with liquidity and entropy constraints. Among them, the risk index is selected as the risk measure which considers the risk-free interest rate. Then, through the different uncertainty distributions of uncertain variables, the uncertain bi-objective portfolio model is transformed into different crisp forms. Furthermore, we construct an uncertain BCC-DEA model to evaluate the uncertain bi-objective portfolio model. Finally, some numerical simulations are given to illustrate the effectiveness and practicality of the presented uncertain bi-objective portfolio model and BCC-DEA model based on the bi-objective genetic algorithm.
{"title":"Uncertain bi-objective portfolio programming models of risky assets with liquidity and entropy constraints under uncertainty theory based DEA efficiency measures","authors":"Bo Li, Qinglong Gao","doi":"10.1016/j.cam.2024.116442","DOIUrl":"10.1016/j.cam.2024.116442","url":null,"abstract":"<div><div>Portfolio optimization is an important class of decision management problems. In addition, data envelopment analysis method is often used to evaluate the pros and cons of the portfolio. In this paper, we propose a bi-objective portfolio model based on uncertainty theory, and present an uncertain Banker–Charnes–Cooper-data envelopment analysis (BCC-DEA) model to evaluate uncertain portfolios of risky assets. Firstly, we propose an uncertain bi-objective portfolio model with liquidity and entropy constraints. Among them, the risk index is selected as the risk measure which considers the risk-free interest rate. Then, through the different uncertainty distributions of uncertain variables, the uncertain bi-objective portfolio model is transformed into different crisp forms. Furthermore, we construct an uncertain BCC-DEA model to evaluate the uncertain bi-objective portfolio model. Finally, some numerical simulations are given to illustrate the effectiveness and practicality of the presented uncertain bi-objective portfolio model and BCC-DEA model based on the bi-objective genetic algorithm.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"461 ","pages":"Article 116442"},"PeriodicalIF":2.1,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143096257","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 : 2024-12-12DOI: 10.1016/j.cam.2024.116430
Ruijie Yin
In this study, we analyze the error estimates for different splitting schemes used in modeling Charged-Particle Dynamics within a strong magnetic field. We introduce an energy-preserving splitting scheme whose per-step computational cost remains unaffected by the magnetic field’s strength. For the maximal ordering scaling case, we establish an error bound for this scheme, and more broadly for a range of Strang splitting schemes, in terms of both position and velocity, which is proportional to the step size . Additionally, we provide an error bound for position and velocity related to the parameter , although this bound is not the most optimal. Numerical experiments are conducted to demonstrate the error characteristics of these splitting schemes, revealing that the error bound exhibits a negative half-order dependence on .
{"title":"Convergence of some conservative Strang splitting methods for Charged-Particle Dynamics under a strong magnetic field","authors":"Ruijie Yin","doi":"10.1016/j.cam.2024.116430","DOIUrl":"10.1016/j.cam.2024.116430","url":null,"abstract":"<div><div>In this study, we analyze the error estimates for different splitting schemes used in modeling Charged-Particle Dynamics within a strong magnetic field. We introduce an energy-preserving splitting scheme whose per-step computational cost remains unaffected by the magnetic field’s strength. For the maximal ordering scaling case, we establish an error bound for this scheme, and more broadly for a range of Strang splitting schemes, in terms of both position and velocity, which is proportional to the step size <span><math><mi>h</mi></math></span>. Additionally, we provide an error bound for position and velocity related to the parameter <span><math><mi>ɛ</mi></math></span>, although this bound is not the most optimal. Numerical experiments are conducted to demonstrate the error characteristics of these splitting schemes, revealing that the error bound exhibits a negative half-order dependence on <span><math><mi>ɛ</mi></math></span>.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116430"},"PeriodicalIF":2.1,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143150050","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 : 2024-12-12DOI: 10.1016/j.cam.2024.116440
Francesco Mezzadri, Emanuele Galligani
In this paper, we introduce the complex-valued horizontal linear complementarity problem (CHLCP), we provide two equivalent real-valued reformulations, and study modulus-based matrix splitting algorithms for solving the CHLCP. This latter point is motivated by the recent introduction of modulus-based matrix splitting methods for (non-horizontal) complex linear complementarity problems (CLCPs), which we generalize. We study the convergence of the proposed algorithms. Whenever possible, we seek convergence conditions that are directly based on the form of the real and imaginary parts of the matrices of the CHLCP in its complex form. This makes the convergence easier to evaluate than in existing convergence analyses. Finally, we study the numerical properties of the proposed algorithms by solving several CHLCPs. In this context, we also revisit results on the CLCP under the larger CHLCP framework, providing new numerical insights on the efficiency of existing algorithms for the CLCP.
{"title":"Modulus-based matrix splitting algorithms for generalized complex-valued horizontal linear complementarity problems","authors":"Francesco Mezzadri, Emanuele Galligani","doi":"10.1016/j.cam.2024.116440","DOIUrl":"10.1016/j.cam.2024.116440","url":null,"abstract":"<div><div>In this paper, we introduce the complex-valued horizontal linear complementarity problem (CHLCP), we provide two equivalent real-valued reformulations, and study modulus-based matrix splitting algorithms for solving the CHLCP. This latter point is motivated by the recent introduction of modulus-based matrix splitting methods for (non-horizontal) complex linear complementarity problems (CLCPs), which we generalize. We study the convergence of the proposed algorithms. Whenever possible, we seek convergence conditions that are directly based on the form of the real and imaginary parts of the matrices of the CHLCP in its complex form. This makes the convergence easier to evaluate than in existing convergence analyses. Finally, we study the numerical properties of the proposed algorithms by solving several CHLCPs. In this context, we also revisit results on the CLCP under the larger CHLCP framework, providing new numerical insights on the efficiency of existing algorithms for the CLCP.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"460 ","pages":"Article 116440"},"PeriodicalIF":2.1,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098736","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}
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