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Adjoint-Based Calibration of Nonlinear Stochastic Differential Equations 基于邻接校准的非线性随机微分方程
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-10-19 DOI: 10.1007/s00245-024-10181-y
Jan Bartsch, Robert Denk, Stefan Volkwein
{"title":"Adjoint-Based Calibration of Nonlinear Stochastic Differential Equations","authors":"Jan Bartsch,&nbsp;Robert Denk,&nbsp;Stefan Volkwein","doi":"10.1007/s00245-024-10181-y","DOIUrl":"10.1007/s00245-024-10181-y","url":null,"abstract":"<div><p>To study the nonlinear properties of complex natural phenomena, the evolution of the quantity of interest can be often represented by systems of coupled nonlinear stochastic differential equations (SDEs). These SDEs typically contain several parameters which have to be chosen carefully to match the experimental data and to validate the effectiveness of the model. In the present paper the calibration of these parameters is described by nonlinear SDE-constrained optimization problems. In the optimize-before-discretize setting a rigorous analysis is carried out to ensure the existence of optimal solutions and to derive necessary first-order optimality conditions. For the numerical solution a Monte–Carlo method is applied using parallelization strategies to compensate for the high computational time. In the numerical examples an Ornstein–Uhlenbeck and a stochastic Prandtl–Tomlinson bath model are considered.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-024-10181-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142451029","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
Optimal Control of a New Class of Parabolic Quasi Variational–Hemivariational Inequality 一类新的抛物线准变-半变量不等式的优化控制
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-10-14 DOI: 10.1007/s00245-024-10190-x
Zhao Jing, Ze Yuan, Zhenhai Liu, Stanislaw Migórski
{"title":"Optimal Control of a New Class of Parabolic Quasi Variational–Hemivariational Inequality","authors":"Zhao Jing,&nbsp;Ze Yuan,&nbsp;Zhenhai Liu,&nbsp;Stanislaw Migórski","doi":"10.1007/s00245-024-10190-x","DOIUrl":"10.1007/s00245-024-10190-x","url":null,"abstract":"<div><p>The primary objective of this paper is to study a new class of parabolic quasi variational–hemivariational inequalities. First, we prove a unique solvability result for such class under some mild conditions. Second, we show the existence of an optimal solution for an associated control problem. Finally, these results are applied to a model of quasistatic frictional contact in mechanics.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431072","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
Locally Lipschitz Stability of Solutions to a Parametric Parabolic Optimal Control Problem with Mixed Pointwise Constraints 具有混合点式约束条件的参数抛物线优化控制问题解的局部 Lipschitz 稳定性
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-10-14 DOI: 10.1007/s00245-024-10191-w
Huynh Khanh
{"title":"Locally Lipschitz Stability of Solutions to a Parametric Parabolic Optimal Control Problem with Mixed Pointwise Constraints","authors":"Huynh Khanh","doi":"10.1007/s00245-024-10191-w","DOIUrl":"10.1007/s00245-024-10191-w","url":null,"abstract":"<div><p>A class of parametric optimal control problems governed by semilinear parabolic equations with mixed pointwise constraints is investigated. The perturbations appear in the objective functional, the state equation and in mixed pointwise constraints. By analyzing regularity and establishing stability condition of Lagrange multipliers we prove that, if the unperturbed problem satisfies the strong second-order sufficient condition, then the solution map and the associated Lagrange multipliers are locally Lipschitz continuous functions of parameters.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142431065","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
Optimality Conditions for Sparse Optimal Control of Viscous Cahn–Hilliard Systems with Logarithmic Potential 具有对数潜力的粘性卡恩-希利亚德系统稀疏最优控制的最优性条件
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-10-10 DOI: 10.1007/s00245-024-10187-6
Pierluigi Colli, Jürgen Sprekels, Fredi Tröltzsch
{"title":"Optimality Conditions for Sparse Optimal Control of Viscous Cahn–Hilliard Systems with Logarithmic Potential","authors":"Pierluigi Colli,&nbsp;Jürgen Sprekels,&nbsp;Fredi Tröltzsch","doi":"10.1007/s00245-024-10187-6","DOIUrl":"10.1007/s00245-024-10187-6","url":null,"abstract":"<div><p>In this paper we study the optimal control of a parabolic initial-boundary value problem of viscous Cahn–Hilliard type with zero Neumann boundary conditions. Phase field systems of this type govern the evolution of diffusive phase transition processes with conserved order parameter. It is assumed that the nonlinear functions driving the physical processes within the spatial domain are double-well potentials of logarithmic type whose derivatives become singular at the boundary of their respective domains of definition. For such systems, optimal control problems have been studied in the past. We focus here on the situation when the cost functional of the optimal control problem contains a nondifferentiable term like the <span>(L^1)</span>-norm, which leads to sparsity of optimal controls. For such cases, we establish first-order necessary and second-order sufficient optimality conditions for locally optimal controls. In the approach to second-order sufficient conditions, the main novelty of this paper, we adapt a technique introduced by Casas et al. in the paper (SIAM J Control Optim 53:2168–2202, 2015). In this paper, we show that this method can also be successfully applied to systems of viscous Cahn–Hilliard type with logarithmic nonlinearity. Since the Cahn–Hilliard system corresponds to a fourth-order partial differential equation in contrast to the second-order systems investigated before, additional technical difficulties have to be overcome.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411164","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
Multiplicative Control Problem for the Stationary Mass Transfer Model with Variable Coefficients 具有可变系数的静态传质模型的乘法控制问题
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-10-07 DOI: 10.1007/s00245-024-10189-4
Evgenii S. Baranovskii, Roman V. Brizitskii, Zhanna Yu. Saritskaia
{"title":"Multiplicative Control Problem for the Stationary Mass Transfer Model with Variable Coefficients","authors":"Evgenii S. Baranovskii,&nbsp;Roman V. Brizitskii,&nbsp;Zhanna Yu. Saritskaia","doi":"10.1007/s00245-024-10189-4","DOIUrl":"10.1007/s00245-024-10189-4","url":null,"abstract":"<div><p>The global existence of a weak solution of a mixed boundary value problem for the stationary mass transfer equations with variable coefficients is proved. The maximum and minimum principle for the substance concentration is established. The solvability of a multiplicative control problem for the considered model is proved.\u0000</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410427","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
Uniform Stabilization for the Semi-linear Wave Equation with Nonlinear Kelvin–Voigt Damping 具有非线性开尔文-沃依格阻尼的半线性波方程的均匀稳定问题
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-10-06 DOI: 10.1007/s00245-024-10186-7
Kaïs Ammari, Marcelo M. Cavalcanti, Sabeur Mansouri
{"title":"Uniform Stabilization for the Semi-linear Wave Equation with Nonlinear Kelvin–Voigt Damping","authors":"Kaïs Ammari,&nbsp;Marcelo M. Cavalcanti,&nbsp;Sabeur Mansouri","doi":"10.1007/s00245-024-10186-7","DOIUrl":"10.1007/s00245-024-10186-7","url":null,"abstract":"<div><p>This paper is concerned with the decay estimate of solutions to the semilinear wave equation subject to two localized dampings in a bounded domain. The first one is of the nonlinear Kelvin–Voigt type which is distributed around a neighborhood of the boundary and the second is a frictional damping depending in the first one. We show uniform decay rate results of the corresponding energy for all initial data taken in bounded sets of finite energy phase-space. The proof is based on obtaining an observability inequality which combines unique continuation properties and the tools of the Microlocal Analysis Theory</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410218","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
Linear Quadratic Nonzero-Sum Mean-Field Stochastic Differential Games with Regime Switching 具有时态转换的线性四次方非零和均值场随机微分博弈
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-10-01 DOI: 10.1007/s00245-024-10188-5
Siyu Lv, Zhen Wu, Jie Xiong
{"title":"Linear Quadratic Nonzero-Sum Mean-Field Stochastic Differential Games with Regime Switching","authors":"Siyu Lv,&nbsp;Zhen Wu,&nbsp;Jie Xiong","doi":"10.1007/s00245-024-10188-5","DOIUrl":"10.1007/s00245-024-10188-5","url":null,"abstract":"<div><p>This paper is concerned with a linear quadratic (LQ) nonzero-sum stochastic differential game for <i>regime switching</i> diffusions with <i>mean-field</i> interactions. The salient features of this paper include that the concept of <i>strategies</i> is first adopted in the LQ nonzero-sum game and <i>conditional</i> mean-field terms appear in the state equation and cost functionals. First, a candidate optimal feedback control-strategy pair for the two players is <i>formally</i> constructed based on solutions of four <i>coupled</i> Riccati equations. Then, we verify that the formal optimal pair is indeed a Nash equilibrium for the game by a delicate <i>multi-step</i> completion of squares. The four Riccati equations introduced in this paper are <i>new</i> in the literature. Uniqueness of solutions to the Riccati equations for the general case and existence of solutions for a special case are obtained. Finally, a numerical example is reported to demonstrate the theoretical results.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409362","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
Zero-Sum Non-stationary Stochastic Games with the Long-Run Average Criterion 具有长期平均标准的零和非稳态随机博弈
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-09-26 DOI: 10.1007/s00245-024-10182-x
Zewu Zheng, Xin Guo
{"title":"Zero-Sum Non-stationary Stochastic Games with the Long-Run Average Criterion","authors":"Zewu Zheng,&nbsp;Xin Guo","doi":"10.1007/s00245-024-10182-x","DOIUrl":"10.1007/s00245-024-10182-x","url":null,"abstract":"<div><p>This paper is concerned with the existence and computation of an equilibrium for a non-stationary average stochastic zero-sum game with Borel spaces, in which the payoff functions and transition probabilities are allowed to change over time. First, we present an extension of the span-fixed point theorem for an operator to a sequence of time-dependent operators. Second, we find a new set of conditions, which is the generalization of the ergodicity ones in the existing literature. Using the extension of the span-fixed point theorem and the novel conditions, we prove the existence of a solution to the average-reward game equations (ARGEs). Third, by the ARGEs we establish the existence of the value and the equilibrium for this game. Moreover,by constructing an approximation sequence of the solution to the ARGEs, we provide a rolling horizon algorithm for computing the value and <span>( varepsilon )</span>-equilibria, and also prove the convergence of the algorithm. Finally, we illustrate the conditions and results in this paper by several energy management models.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414180","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
Stability of Laminated Timoshenko Beams with Local Viscoelastic Versus Frictional Damping 具有局部粘弹性阻尼和摩擦阻尼的层叠式 Timoshenko 梁的稳定性
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-09-22 DOI: 10.1007/s00245-024-10183-w
Yu-Ying Duan, Ti-Jun Xiao
{"title":"Stability of Laminated Timoshenko Beams with Local Viscoelastic Versus Frictional Damping","authors":"Yu-Ying Duan,&nbsp;Ti-Jun Xiao","doi":"10.1007/s00245-024-10183-w","DOIUrl":"10.1007/s00245-024-10183-w","url":null,"abstract":"<div><p>In this paper, we consider a two-layered beam system with an interfacial slip, stabilized only by one viscoelastic vs. frictional damping acting on a small portion of the beam. We show that the <i>local</i> damping is enough to induce the whole dissipation mechanism, and give a general and explicit energy decay rate only under basic conditions on the damping. Meanwhile, we obtain <i>optimal</i> decay rates, when the frictional damping is near linear or polynomial, and the behavior of the memory kernel at infinity is either unquantified or quantified in a quite general way, by means of quantifying the effectiveness of each type of the damping. In order to handle the difficulty caused by the local feature of the damping, we manage to find fitting weighted functions to process region segmentation, as well as to construct appropriate auxiliary functionals. Our results improve and generalize the existing related results for the system to a large extent, and they are novel even for the classical Timoshenko beam system (without slip).</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413222","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
Reconstruction of a Singular Source in a Fractional Subdiffusion Problem from a Single Point Measurement 从单点测量重构分数次扩散问题中的奇异源
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-09-21 DOI: 10.1007/s00245-024-10185-8
M. Hrizi, F. Hajji, R. Prakash, A. A. Novotny
{"title":"Reconstruction of a Singular Source in a Fractional Subdiffusion Problem from a Single Point Measurement","authors":"M. Hrizi,&nbsp;F. Hajji,&nbsp;R. Prakash,&nbsp;A. A. Novotny","doi":"10.1007/s00245-024-10185-8","DOIUrl":"10.1007/s00245-024-10185-8","url":null,"abstract":"<div><p>In this paper, we reconstruct a singular time dependent source function of a fractional subdiffusion problem using observational data obtained from a single point of the boundary and inside of the domain. Specifically, the singular function under consideration is represented by the Dirac delta function which makes the analysis interesting as the temporal component of unknown source belongs to a Sobolev space of negative order. We establish the uniqueness of the examined inverse problem in both scenarios. In addition, we analyze local stability of the solution of our inverse problem. To numerically reconstruct a point-wise source, we use the techniques of topological derivatives by converting the inverse source problem in an optimization one. More precisely, we develop a second-order non-iterative reconstruction algorithm to achieve our goal. The efficacy of the proposed approach is substantiated through diverse numerical examples.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412991","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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