Pub Date : 2024-11-07DOI: 10.1016/j.cam.2024.116347
Jie Chen, Haoxuan Li, Xiangfeng Yang
Uncertain geometric programming is a type of geometric programming involving uncertain variables. As described in the literature, the uncertain geometric programming model based on expected value cannot reflect the risk preference of decision-makers. It motivates us to establish an uncertain geometric programming model based on value-at-risk to describe the risk level that managers can tolerate. Firstly, we propose the uncertain geometric programming model based on value-at-risk. Then, according to the operational law in uncertainty theory, this model is transformed into a crisp and equivalent form. Three numerical examples are used to verify the model’s efficacy, and the paper emphasizes the influence of confidence level in the objective function and the constraints. In addition, the paper discusses the expected value model under an uncertain environment and presents the difference between expected value and value-at-risk. Finally, we apply the model to the problem of a two-bar truss, and the optimal solution can be obtained within the risk level that the structural designer can accept.
{"title":"An efficient uncertain chance constrained geometric programming model based on value-at-risk for truss structure optimization problems","authors":"Jie Chen, Haoxuan Li, Xiangfeng Yang","doi":"10.1016/j.cam.2024.116347","DOIUrl":"10.1016/j.cam.2024.116347","url":null,"abstract":"<div><div>Uncertain geometric programming is a type of geometric programming involving uncertain variables. As described in the literature, the uncertain geometric programming model based on expected value cannot reflect the risk preference of decision-makers. It motivates us to establish an uncertain geometric programming model based on value-at-risk to describe the risk level that managers can tolerate. Firstly, we propose the uncertain geometric programming model based on value-at-risk. Then, according to the operational law in uncertainty theory, this model is transformed into a crisp and equivalent form. Three numerical examples are used to verify the model’s efficacy, and the paper emphasizes the influence of confidence level in the objective function and the constraints. In addition, the paper discusses the expected value model under an uncertain environment and presents the difference between expected value and value-at-risk. Finally, we apply the model to the problem of a two-bar truss, and the optimal solution can be obtained within the risk level that the structural designer can accept.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116347"},"PeriodicalIF":2.1,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652787","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 : 2024-11-07DOI: 10.1016/j.cam.2024.116345
Min Xu , Zhongfeng Qin , Junbin Wang
Cluster analysis is an essential method in machine learning, primarily used in situations with crisp data. However, data obtained in practice can be imprecise, forcing classic clustering methods to fail. Spurred by this constraint, this paper introduces an uncertain c-means clustering method, which employs uncertain variables to characterize imprecise observations based on the uncertainty theory. Specifically, we define a distance from an uncertain variable to a crisp vector and introduce an uncertain partition method. Additionally, according to the distance and partition method, an uncertain clustering is proposed. Finally, numerical experiments demonstrate the effectiveness of the proposed method.
{"title":"Uncertain c-means clustering method with application to imprecise observations","authors":"Min Xu , Zhongfeng Qin , Junbin Wang","doi":"10.1016/j.cam.2024.116345","DOIUrl":"10.1016/j.cam.2024.116345","url":null,"abstract":"<div><div>Cluster analysis is an essential method in machine learning, primarily used in situations with crisp data. However, data obtained in practice can be imprecise, forcing classic clustering methods to fail. Spurred by this constraint, this paper introduces an uncertain c-means clustering method, which employs uncertain variables to characterize imprecise observations based on the uncertainty theory. Specifically, we define a distance from an uncertain variable to a crisp vector and introduce an uncertain partition method. Additionally, according to the distance and partition method, an uncertain clustering is proposed. Finally, numerical experiments demonstrate the effectiveness of the proposed method.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"459 ","pages":"Article 116345"},"PeriodicalIF":2.1,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142661500","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 : 2024-11-05DOI: 10.1016/j.cam.2024.116338
Xuexue Chen , Cuilian You
Reference price (quality) is a benchmark point used by consumers to make price (quality) judgements. Combining reference price and reference quality with dynamic pricing and inventory management, this paper applies differential equations theory to construct a optimal control model for perishable products when the quality of products declines exponentially. The demand of products depends on price, quality, reference price and reference quality, among which reference price and reference quality are influenced by consumers’ past memory. The aim is to maximize the retailer’s profit during the period. The conclusions are as follows. Firstly, a optimal dynamic pricing and inventory model for perishable products with reference price and reference quality is constructed, and the model is extended to dual decision variables, stochastic demand, time-dependent effects, competitive and infinite planing horizon setups. Secondly, through the Pontryagin maximum principle, the analytical expression of the optimal dynamic price is derived. Thirdly, a linear search method to solve the optimal static price is proposed. Finally, the sensitivity of the main parameters is analyzed and the corresponding management enlightenments are given. By comparison of dynamic and static pricing, we find that dynamic pricing can achieve more profits and take a shorter selling period. In addition, for the sales problem of perishable products affected by both reference price and reference quality, retailers should adopt skimming pricing strategy (the optimal price decreases with time). Furthermore, to obtain more profit, retails should strive to increase the sensitivity coefficients of two types of reference, and the reference quality memory coefficient, while to decrease the reference price memory coefficient.
{"title":"Dynamic pricing and inventory model for perishable products with reference price and reference quality","authors":"Xuexue Chen , Cuilian You","doi":"10.1016/j.cam.2024.116338","DOIUrl":"10.1016/j.cam.2024.116338","url":null,"abstract":"<div><div>Reference price (quality) is a benchmark point used by consumers to make price (quality) judgements. Combining reference price and reference quality with dynamic pricing and inventory management, this paper applies differential equations theory to construct a optimal control model for perishable products when the quality of products declines exponentially. The demand of products depends on price, quality, reference price and reference quality, among which reference price and reference quality are influenced by consumers’ past memory. The aim is to maximize the retailer’s profit during the period. The conclusions are as follows. Firstly, a optimal dynamic pricing and inventory model for perishable products with reference price and reference quality is constructed, and the model is extended to dual decision variables, stochastic demand, time-dependent effects, competitive and infinite planing horizon setups. Secondly, through the Pontryagin maximum principle, the analytical expression of the optimal dynamic price is derived. Thirdly, a linear search method to solve the optimal static price is proposed. Finally, the sensitivity of the main parameters is analyzed and the corresponding management enlightenments are given. By comparison of dynamic and static pricing, we find that dynamic pricing can achieve more profits and take a shorter selling period. In addition, for the sales problem of perishable products affected by both reference price and reference quality, retailers should adopt skimming pricing strategy (the optimal price decreases with time). Furthermore, to obtain more profit, retails should strive to increase the sensitivity coefficients of two types of reference, and the reference quality memory coefficient, while to decrease the reference price memory coefficient.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116338"},"PeriodicalIF":2.1,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652786","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 : 2024-11-02DOI: 10.1016/j.cam.2024.116346
Mo Faheem, Bapan Ghosh
Existing literature established stability in a delayed logistic Lotka–Volterra predator–prey model in terms of equilibrium analysis. However, several researchers did not construct the time-series analysis in such models. It has also been observed that both the RK4 methods and the inbuilt ‘dde23’ MATLAB solver were unable to generate stable solutions. This motivated us to develop a nonstandard scheme to capture the numerical solutions which are well consistent with the analytical equilibrium analysis of continuous delayed predator–prey model. In this paper, we will propose a nonstandard finite difference (NSFD) scheme for a delayed predator–prey model. We shall prove that the developed scheme preserves the qualitative behavior of the system, including the local stability of the equilibrium, and stability switching for any step size . It is observed that the discretized system shows the occurrence of a Neimark-Sacker bifurcation. Moreover, the convergence analysis of the numerical scheme establishes first-order convergence. The bifurcation diagram and comparison of delay sequence generated by NSFD with the ones obtained by analytical means have been discussed graphically.
{"title":"Dynamics of a delayed discrete-time predator prey model proposed from a nonstandard finite difference scheme","authors":"Mo Faheem, Bapan Ghosh","doi":"10.1016/j.cam.2024.116346","DOIUrl":"10.1016/j.cam.2024.116346","url":null,"abstract":"<div><div>Existing literature established stability in a delayed logistic Lotka–Volterra predator–prey model in terms of equilibrium analysis. However, several researchers did not construct the time-series analysis in such models. It has also been observed that both the RK4 methods and the inbuilt ‘dde23’ MATLAB solver were unable to generate stable solutions. This motivated us to develop a nonstandard scheme to capture the numerical solutions which are well consistent with the analytical equilibrium analysis of continuous delayed predator–prey model. In this paper, we will propose a nonstandard finite difference (NSFD) scheme for a delayed predator–prey model. We shall prove that the developed scheme preserves the qualitative behavior of the system, including the local stability of the equilibrium, and stability switching for any step size <span><math><mrow><mi>h</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>m</mi></mrow></mfrac><mo>,</mo><mspace></mspace><mi>m</mi><mo>∈</mo><msup><mrow><mi>Z</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math></span>. It is observed that the discretized system shows the occurrence of a Neimark-Sacker bifurcation. Moreover, the convergence analysis of the numerical scheme establishes first-order convergence. The bifurcation diagram and comparison of delay <span><math><mrow><mi>τ</mi><mo>−</mo></mrow></math></span>sequence generated by NSFD with the ones obtained by analytical means have been discussed graphically.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116346"},"PeriodicalIF":2.1,"publicationDate":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142652785","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 : 2024-11-02DOI: 10.1016/j.cam.2024.116342
Yuexin Yu
General linear methods are adapted for solving nonlinear neutral delay integro-differential equations. The sufficient conditions for the stability and asymptotic stability of -algebraically stable general linear methods are derived. At last, a numerical test is given to validate the theoretical results.
{"title":"Solving nonlinear neutral delay integro-differential equations via general linear methods","authors":"Yuexin Yu","doi":"10.1016/j.cam.2024.116342","DOIUrl":"10.1016/j.cam.2024.116342","url":null,"abstract":"<div><div>General linear methods are adapted for solving nonlinear neutral delay integro-differential equations. The sufficient conditions for the stability and asymptotic stability of <span><math><mrow><mo>(</mo><mi>k</mi><mo>,</mo><mi>l</mi><mo>)</mo></mrow></math></span>-algebraically stable general linear methods are derived. At last, a numerical test is given to validate the theoretical results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116342"},"PeriodicalIF":2.1,"publicationDate":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586301","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 : 2024-10-29DOI: 10.1016/j.cam.2024.116325
Eduardo Abreu , Richard De la cruz , Juan Juajibioy , Wanderson Lambert
<div><div>In this work, we have expanded upon the (local) semi-discrete Lagrangian-Eulerian method initially introduced in Abreu et al. (2022) to approximate a specific class of multi-dimensional scalar conservation laws with nonlocal flux, referred to as the nonlocal model: <span><math><mrow><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>ρ</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>+</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>d</mi></mrow></msubsup><msub><mrow><mi>∂</mi></mrow><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mrow><mo>(</mo><mrow><msup><mrow><mi>V</mi></mrow><mrow><mi>i</mi></mrow></msup><mrow><mo>[</mo><mrow><mi>W</mi><mrow><mo>[</mo><mi>ρ</mi><mo>,</mo><mi>ω</mi><mo>]</mo></mrow><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow><mo>]</mo></mrow><msup><mrow><mi>F</mi></mrow><mrow><mi>i</mi></mrow></msup><mrow><mo>(</mo><mi>ρ</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mo>)</mo></mrow><mo>=</mo><mn>0</mn><mo>,</mo><mspace></mspace><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo></mrow><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>.</mo></mrow></math></span> For completeness, we analyze the convergence of this method using the weak asymptotic approach introduced in Abreu et al. (2016), with significant results extended to the multidimensional nonlocal case. While there are indeed other important techniques available that can be utilized to prove the convergence of the numerical scheme, the choice of this particular technique (weak asymptotic analysis) is quite natural. This is primarily due to its suitability for dealing with the Lagrangian-Eulerian schemes proposed in this paper. Essentially, the weak asymptotic method generates a family of approximate solutions satisfying the following properties: 1) The family of approximate functions is uniformly bounded in the space <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow><mo>∩</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>. 2) The family is dominated by a suitable temporal and spatial modulus of continuity. These properties allow us to employ the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-compactness argument to extract a convergent subsequence. We demonstrate that the limit function is a weak entropy solution of Eq. <span><span>(1)</span></span>. Finally, we present a section of numerical examples to illustrate our results. Finally, we have examined examples discussed in Aggarwal et al. (2015) and Keime
{"title":"Semi-discrete Lagrangian-Eulerian approach based on the weak asymptotic method for nonlocal conservation laws in several dimensions","authors":"Eduardo Abreu , Richard De la cruz , Juan Juajibioy , Wanderson Lambert","doi":"10.1016/j.cam.2024.116325","DOIUrl":"10.1016/j.cam.2024.116325","url":null,"abstract":"<div><div>In this work, we have expanded upon the (local) semi-discrete Lagrangian-Eulerian method initially introduced in Abreu et al. (2022) to approximate a specific class of multi-dimensional scalar conservation laws with nonlocal flux, referred to as the nonlocal model: <span><math><mrow><msub><mrow><mi>∂</mi></mrow><mrow><mi>t</mi></mrow></msub><mi>ρ</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>+</mo><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>d</mi></mrow></msubsup><msub><mrow><mi>∂</mi></mrow><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msub><mrow><mo>(</mo><mrow><msup><mrow><mi>V</mi></mrow><mrow><mi>i</mi></mrow></msup><mrow><mo>[</mo><mrow><mi>W</mi><mrow><mo>[</mo><mi>ρ</mi><mo>,</mo><mi>ω</mi><mo>]</mo></mrow><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow><mo>]</mo></mrow><msup><mrow><mi>F</mi></mrow><mrow><mi>i</mi></mrow></msup><mrow><mo>(</mo><mi>ρ</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow><mo>)</mo></mrow><mo>=</mo><mn>0</mn><mo>,</mo><mspace></mspace><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo></mrow><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>.</mo></mrow></math></span> For completeness, we analyze the convergence of this method using the weak asymptotic approach introduced in Abreu et al. (2016), with significant results extended to the multidimensional nonlocal case. While there are indeed other important techniques available that can be utilized to prove the convergence of the numerical scheme, the choice of this particular technique (weak asymptotic analysis) is quite natural. This is primarily due to its suitability for dealing with the Lagrangian-Eulerian schemes proposed in this paper. Essentially, the weak asymptotic method generates a family of approximate solutions satisfying the following properties: 1) The family of approximate functions is uniformly bounded in the space <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow><mo>∩</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>. 2) The family is dominated by a suitable temporal and spatial modulus of continuity. These properties allow us to employ the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-compactness argument to extract a convergent subsequence. We demonstrate that the limit function is a weak entropy solution of Eq. <span><span>(1)</span></span>. Finally, we present a section of numerical examples to illustrate our results. Finally, we have examined examples discussed in Aggarwal et al. (2015) and Keime","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116325"},"PeriodicalIF":2.1,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586653","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 : 2024-10-29DOI: 10.1016/j.cam.2024.116343
Josefa Caballero , Hanna Okrasińska-Płociniczak , Łukasz Płociniczak , Kishin Sadarangani
We consider a nonlocal functional equation that is a generalization of the mathematical model used in behavioral sciences. The equation is built upon an operator that introduces a convex combination and a nonlinear mixing of the function arguments. We show that, provided some growth conditions of the coefficients, there exists a unique solution in the natural Lipschitz space. Furthermore, we prove that the regularity of the solution is inherited from the smoothness properties of the coefficients.
As a natural numerical method to solve the general case, we consider the collocation scheme of piecewise linear functions. We prove that the method converges with the error bounded by the error of projecting the Lipschitz function onto the piecewise linear polynomial space. Moreover, provided sufficient regularity of the coefficients, the scheme is of the second order measured in the supremum norm.
A series of numerical experiments verify the proved claims and show that the implementation is computationally cheap and exceeds the frequently used Picard iteration by orders of magnitude in the calculation time.
{"title":"Collocation method for a functional equation arising in behavioral sciences","authors":"Josefa Caballero , Hanna Okrasińska-Płociniczak , Łukasz Płociniczak , Kishin Sadarangani","doi":"10.1016/j.cam.2024.116343","DOIUrl":"10.1016/j.cam.2024.116343","url":null,"abstract":"<div><div>We consider a nonlocal functional equation that is a generalization of the mathematical model used in behavioral sciences. The equation is built upon an operator that introduces a convex combination and a nonlinear mixing of the function arguments. We show that, provided some growth conditions of the coefficients, there exists a unique solution in the natural Lipschitz space. Furthermore, we prove that the regularity of the solution is inherited from the smoothness properties of the coefficients.</div><div>As a natural numerical method to solve the general case, we consider the collocation scheme of piecewise linear functions. We prove that the method converges with the error bounded by the error of projecting the Lipschitz function onto the piecewise linear polynomial space. Moreover, provided sufficient regularity of the coefficients, the scheme is of the second order measured in the supremum norm.</div><div>A series of numerical experiments verify the proved claims and show that the implementation is computationally cheap and exceeds the frequently used Picard iteration by orders of magnitude in the calculation time.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116343"},"PeriodicalIF":2.1,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572663","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 : 2024-10-28DOI: 10.1016/j.cam.2024.116336
Hongzhi Tong
In this paper we consider the robust regression problem when the output variable may be heavy-tailed. In such scenarios, the traditional least squares regression paradigm is usually thought to be not a good choice as it lacks robustness to outliers. By projecting the outputs onto an adaptive interval, we show the regularized least squares regression can still work well when the conditional distribution satisfies a weak moment condition. Fast convergence rates in various norm are derived by tuning the projection scale parameter and regularization parameter in according with the sample size and the moment condition.
{"title":"Least squares regression under weak moment conditions","authors":"Hongzhi Tong","doi":"10.1016/j.cam.2024.116336","DOIUrl":"10.1016/j.cam.2024.116336","url":null,"abstract":"<div><div>In this paper we consider the robust regression problem when the output variable may be heavy-tailed. In such scenarios, the traditional least squares regression paradigm is usually thought to be not a good choice as it lacks robustness to outliers. By projecting the outputs onto an adaptive interval, we show the regularized least squares regression can still work well when the conditional distribution satisfies a weak moment condition. Fast convergence rates in various norm are derived by tuning the projection scale parameter and regularization parameter in according with the sample size and the moment condition.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116336"},"PeriodicalIF":2.1,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142561278","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 : 2024-10-28DOI: 10.1016/j.cam.2024.116330
Gianluca Frasca-Caccia
A new technique has been recently introduced to define finite difference schemes that preserve local conservation laws. So far, this approach has been applied to find parametric families of numerical methods with polynomial conservation laws. This paper extends the existing approach to preserve non polynomial conservation laws. Although the approach is general, the treatment of the nonlinear terms depends on the problem at hand. New parameter depending families of conservative schemes are here introduced for the sine–Gordon equation and a magma equation. Optimal methods in each family are identified by finding values of the parameters that minimize a defect-based approximation of the local error in the time discretization.
{"title":"Finite difference schemes with non polynomial local conservation laws","authors":"Gianluca Frasca-Caccia","doi":"10.1016/j.cam.2024.116330","DOIUrl":"10.1016/j.cam.2024.116330","url":null,"abstract":"<div><div>A new technique has been recently introduced to define finite difference schemes that preserve local conservation laws. So far, this approach has been applied to find parametric families of numerical methods with polynomial conservation laws. This paper extends the existing approach to preserve non polynomial conservation laws. Although the approach is general, the treatment of the nonlinear terms depends on the problem at hand. New parameter depending families of conservative schemes are here introduced for the sine–Gordon equation and a magma equation. Optimal methods in each family are identified by finding values of the parameters that minimize a defect-based approximation of the local error in the time discretization.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116330"},"PeriodicalIF":2.1,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578376","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 : 2024-10-28DOI: 10.1016/j.cam.2024.116341
Nguyen Buong
In this paper, we study the variational inequality problem over the set of common fixed points of a Lipschitz continuous pseudo-contraction and a finite family of strictly pseudo-contractive operators on a real Hilbert space. We introduce a first order dynamical system in accordance with the Lavrentiev regularization method. The existence and strong convergence with a discretized variant of the trajectory of the dynamical system are proved under some mild conditions. Applications to solving the convex constrained monotone equations and to the LASSO problem with numerical experiments are given for validating our results.
{"title":"A first order dynamical system and its discretization for a class of variational inequalities","authors":"Nguyen Buong","doi":"10.1016/j.cam.2024.116341","DOIUrl":"10.1016/j.cam.2024.116341","url":null,"abstract":"<div><div>In this paper, we study the variational inequality problem over the set of common fixed points of a Lipschitz continuous pseudo-contraction and a finite family of strictly pseudo-contractive operators on a real Hilbert space. We introduce a first order dynamical system in accordance with the Lavrentiev regularization method. The existence and strong convergence with a discretized variant of the trajectory of the dynamical system are proved under some mild conditions. Applications to solving the convex constrained monotone equations and to the LASSO problem with numerical experiments are given for validating our results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116341"},"PeriodicalIF":2.1,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572662","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号