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Regularity and Stabilization of Magneto-Elastic Systems 磁弹性系统的正则性与稳定性
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-05-26 DOI: 10.1007/s00245-025-10271-5
Jaime E. Muñoz Rivera, Reinhard Racke
{"title":"Regularity and Stabilization of Magneto-Elastic Systems","authors":"Jaime E. Muñoz Rivera,&nbsp;Reinhard Racke","doi":"10.1007/s00245-025-10271-5","DOIUrl":"10.1007/s00245-025-10271-5","url":null,"abstract":"<div><p>We consider the mathematical model for a plate in a bounded reference configuration <span>(Omega subset mathbb {R}^n)</span>, first with <span>(n=2)</span>, which is interacting with <span>(n=2)</span> magnetic fields. The latter have a damping effect. It will be shown that the arising system generates an analytic semigroup and that the estimated exponential decay rate tends to zero if the <i>n</i> constant directing magnetic vectors tend to become linearly dependent. Then, an analogous model for <span>(n=3)</span> will be considered. In the case that there are less than <i>n</i> magnetic fields we prove the strong stability exemplarily for cubes.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144135278","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}
引用次数: 0
Carleman Estimates and Exact Controllability Results for a Transmission System of two Nonconservative wave Equations 两个非保守波动方程传输系统的Carleman估计和精确可控性结果
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-05-21 DOI: 10.1007/s00245-025-10270-6
Carole Louis-Rose, Ali Perina, Louis Tebou
{"title":"Carleman Estimates and Exact Controllability Results for a Transmission System of two Nonconservative wave Equations","authors":"Carole Louis-Rose,&nbsp;Ali Perina,&nbsp;Louis Tebou","doi":"10.1007/s00245-025-10270-6","DOIUrl":"10.1007/s00245-025-10270-6","url":null,"abstract":"<div><p>We consider a transmission system of two nonconservative wave equations with nonconstant coefficients in the one-dimensional setting. We investigate the exact (boundary and internal) controllability of this system using a single control. To solve these exact controllability problems, we rely on the duality approach which consists in proving inverse or observability inequality for the corresponding adjoint system. To prove these observability inequalities, we establish new Carleman estimates for the corresponding uncontrolled transmission system. These Carleman estimates require the introduction of new weight functions adapted to the coefficients of the principal operators. In particular, our Carleman estimates with internal observation are new in the framework of transmission systems.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144108488","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}
引用次数: 0
Bilevel Optimization of the Kantorovich Problem and Its Quadratic Regularization Kantorovich问题的双层优化及其二次正则化
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-05-15 DOI: 10.1007/s00245-025-10264-4
Sebastian Hillbrecht, Christian Meyer
{"title":"Bilevel Optimization of the Kantorovich Problem and Its Quadratic Regularization","authors":"Sebastian Hillbrecht,&nbsp;Christian Meyer","doi":"10.1007/s00245-025-10264-4","DOIUrl":"10.1007/s00245-025-10264-4","url":null,"abstract":"<div><p>This paper is concerned with an optimization problem which is governed by the Kantorovich problem of optimal transport. More precisely, we consider a bilevel optimization problem with the underlying problem being the Kantorovich problem. This task can be reformulated as a mathematical problem with complementarity constraints in the space of regular Borel measures. Because of the non-smoothness that is induced by the complementarity constraints, problems of this type are often regularized, e.g., by an entropic regularization. However, in this paper we apply a quadratic regularization to the Kantorovich problem. By doing so, we are able to drastically reduce its dimension while preserving the sparsity structure of the optimal transportation plan as much as possible. As the title indicates, this is the first part of a series of three papers. It deals with the existence of optimal solutions to the bilevel problem and its quadratic regularization, while Parts II and III are devoted to convergence analysis for the vanishing regularization parameters.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144074005","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}
引用次数: 0
Optimal Investment and Reinsurance of Insurers with a Nonlinear Stochastic Factor Model 基于非线性随机因子模型的保险公司最优投资与再保险
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-05-12 DOI: 10.1007/s00245-025-10265-3
Hiroaki Hata
{"title":"Optimal Investment and Reinsurance of Insurers with a Nonlinear Stochastic Factor Model","authors":"Hiroaki Hata","doi":"10.1007/s00245-025-10265-3","DOIUrl":"10.1007/s00245-025-10265-3","url":null,"abstract":"<div><p>In this paper, we consider an optimal investment and reinsurance problem faced by an insurer. The insurer invests in a market consisting of a riskless asset and <i>m</i> risky assets. The mean returns and volatilities of the risky assets depend nonlinearly on economic factors. These factors are formulated as the solutions of nonlinear stochastic differential equations. The wealth of the insurer is described by the riskless asset, the risky assets, and a Cramér–Lundberg process for reinsurance. Moreover, the insurer’s preferences are described by an exponential utility function [i.e., CARA (Constant Absolute Risk Aversion) utility function]. By adapting the dynamic programming approach, we derive the Hamilton–Jacobi–Bellman (HJB) equation. We also prove the solvability of the HJB equation by approximating it with a sequence of related Dirichlet problems or by using the extended Feynman–Kac formula. Finally, by proving the verification theorem, we construct the optimal strategy. Additionally, the optimal reinsurance strategy, which is a deterministic function, is developed. The optimal strategy is further obtained using the stochastic maximum principle, coupled forward and backward stochastic differential equations (FBSDEs), and by proving the verification theorem.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143938182","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}
引用次数: 0
Observer-Based Exponential Stability of the Fractional Heat Equation 基于观测器的分数阶热方程的指数稳定性
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-05-10 DOI: 10.1007/s00245-025-10266-2
Hugo Parada
{"title":"Observer-Based Exponential Stability of the Fractional Heat Equation","authors":"Hugo Parada","doi":"10.1007/s00245-025-10266-2","DOIUrl":"10.1007/s00245-025-10266-2","url":null,"abstract":"<div><p>In this work, the exponential stability of the nonlocal fractional heat equation is studied. The fractional Laplacian is defined via a singular integral. Using the spectral properties of the fractional Laplacian and a state decomposition, a feedback control is constructed by considering the first <i>N</i> modes and an observer defined via a bounded operator. Different configurations are examined, including interior controller with interior observation, and interior controller with exterior observation. Using the recent result about the simplicity of the eigenvalues (Fall et al. in Calc Var Partial Differ Equ 62(8):233, 2023), some of our stabilization results are valid for <span>(sin (0,1))</span>, in particular for <span>(sin (0,1/2))</span> in which case the fractional heat equation is not null controllable.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10266-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143932322","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}
引用次数: 0
Quantitative Convergence of Quadratically Regularized Linear Programs 二次正则化线性规划的定量收敛性
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-05-10 DOI: 10.1007/s00245-025-10267-1
Alberto González-Sanz, Marcel Nutz
{"title":"Quantitative Convergence of Quadratically Regularized Linear Programs","authors":"Alberto González-Sanz,&nbsp;Marcel Nutz","doi":"10.1007/s00245-025-10267-1","DOIUrl":"10.1007/s00245-025-10267-1","url":null,"abstract":"<div><p>Linear programs with quadratic (“ridge”) regularization are of recent interest in optimal transport: unlike entropic regularization, the squared-norm penalty gives rise to sparse approximations of optimal transport couplings. More broadly, quadratic regularization is used in overparametrized learning problems to single out a particular solution. It is well known that the solution of a quadratically regularized linear program over any polytope converges stationarily to the minimal-norm solution of the linear program when the regularization parameter tends to zero. However, that result is merely qualitative. Our main result quantifies the convergence by specifying the exact threshold for the regularization parameter, after which the regularized solution also solves the linear program. Moreover, we bound the suboptimality of the regularized solution before the threshold. These results are complemented by a convergence rate for the regime of large regularization. We apply our general results to the setting of optimal transport, where we shed light on how the threshold and suboptimality depend on the number of data points.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143932323","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}
引用次数: 0
Finite Element Approximation of Lyapunov Equations Related to Parabolic Stochastic PDEs 抛物型随机偏微分方程Lyapunov方程的有限元逼近
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-05-03 DOI: 10.1007/s00245-025-10260-8
Adam Andersson, Annika Lang, Andreas Petersson, Leander Schroer
{"title":"Finite Element Approximation of Lyapunov Equations Related to Parabolic Stochastic PDEs","authors":"Adam Andersson,&nbsp;Annika Lang,&nbsp;Andreas Petersson,&nbsp;Leander Schroer","doi":"10.1007/s00245-025-10260-8","DOIUrl":"10.1007/s00245-025-10260-8","url":null,"abstract":"<div><p>A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear stochastic partial differential equations (SPDEs) driven by multiplicative noise is considered. The discretization of the Lyapunov equation in space is given by finite elements and in time by a semiimplicit Euler scheme. The main result is the derivation of the rate of convergence in operator norm. Moreover, it is shown that the solution of the equation provides a representation of a quadratic and path dependent functional of the SPDE solution. This fact yields a deterministic numerical method to compute such functionals. As a secondary result, weak error rates are established for a fully discrete finite element approximation of the SPDE with respect to this functional. This is obtained as a consequence of the approximation analysis of the Lyapunov equation. It is the first weak convergence analysis for fully discrete finite element approximations of SPDEs driven by multiplicative noise that obtains double the strong rate of convergence, especially for path dependent functionals and smooth spatial noise. Numerical experiments illustrate the results empirically, and it is demonstrated that the deterministic method has advantages over Monte Carlo sampling in a stability context.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10260-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143900786","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}
引用次数: 0
The (alpha )-Dependence of the Invariant Measure for the Stochastic Navier–Stokes Equation Driven by (alpha )-Stable Lévy Processes (alpha ) -稳定l<s:1>过程驱动的随机Navier-Stokes方程的(alpha ) -依赖性不变测度
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-04-30 DOI: 10.1007/s00245-025-10259-1
Ting Li, Xianming Liu
{"title":"The (alpha )-Dependence of the Invariant Measure for the Stochastic Navier–Stokes Equation Driven by (alpha )-Stable Lévy Processes","authors":"Ting Li,&nbsp;Xianming Liu","doi":"10.1007/s00245-025-10259-1","DOIUrl":"10.1007/s00245-025-10259-1","url":null,"abstract":"<div><p>Our study focuses on the convergence behavior of invariant measures associated with Navier–Stokes equations forced by cylindrical <span>(alpha )</span>-stable noises, which could be either non-degenerate or degenerate. Despite the absence of uniqueness in the invariant measures, we successfully demonstrate the convergence of invariant measures from both non-degenerate and degenerate noise cases to their corresponding Navier–Stokes equations driven by Brownian motions as <span>(alpha )</span> tends to 2, under the Wasserstein metric. Especially, for the non-degenerate case, the convergence of invariant measures is established in the sense of the Wasserstein-1 metric.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10259-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143892671","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}
引用次数: 0
Weak Closed-Loop Solvability of Linear Quadratic Stochastic Optimal Control Problems with Partial Information 部分信息线性二次型随机最优控制问题的弱闭环可解性
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-04-27 DOI: 10.1007/s00245-025-10262-6
Xun Li, Guangchen Wang, Jie Xiong, Heng Zhang
{"title":"Weak Closed-Loop Solvability of Linear Quadratic Stochastic Optimal Control Problems with Partial Information","authors":"Xun Li,&nbsp;Guangchen Wang,&nbsp;Jie Xiong,&nbsp;Heng Zhang","doi":"10.1007/s00245-025-10262-6","DOIUrl":"10.1007/s00245-025-10262-6","url":null,"abstract":"<div><p>This paper investigates a linear quadratic stochastic optimal control (LQSOC) problem with partial information. Firstly, by introducing two Riccati equations and a backward stochastic differential equation (BSDE), we solve this LQSOC problem under standard positive semidefinite assumptions. Secondly, by means of a perturbation approach, we study open-loop solvability of this problem when the weighting matrices in the cost functional are indefinite. Thirdly, we investigate weak closed-loop solvability of this problem and prove the equivalence between open-loop and weak closed-loop solvabilities. Finally, we give an example to illustrate the way for obtaining a weak closed-loop optimal strategy.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143877687","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}
引用次数: 0
A Non Linear Optimal Control Problem Related to a Road De-icing Device: Analysis and Numerical Experiments 道路除冰装置的非线性最优控制问题：分析与数值实验
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-04-27 DOI: 10.1007/s00245-025-10261-7
Frédéric Bernardin, Jérôme Lemoine, Arnaud Münch
{"title":"A Non Linear Optimal Control Problem Related to a Road De-icing Device: Analysis and Numerical Experiments","authors":"Frédéric Bernardin,&nbsp;Jérôme Lemoine,&nbsp;Arnaud Münch","doi":"10.1007/s00245-025-10261-7","DOIUrl":"10.1007/s00245-025-10261-7","url":null,"abstract":"<div><p>In order to design a road de-icing device by heating, we consider in a two dimensional setting the optimal control of an advection–diffusion equation with a nonlinear boundary condition of the Stefan-Boltzmann type. The problem models the heating of a road during a winter period to keep positive its surface temperature above a given threshold. The heating device is performed through the circulation of a coolant in a porous layer of the road. We prove the well-posedeness of the nonlinear optimal control problem, subject to unilateral constraints on the control and the state, set up a gradient based algorithm then discuss some numerical results associated with real data obtained from experimental measurements. The study, initially developed in a one dimensional simpler setting in [1], aims to quantify the minimal energy to be provided to keep the road surface without frost or snow.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143879520","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}
引用次数: 0
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