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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
Well-Posedness of Infinite Horizon FBSDEs with Non-zero Terminals and LQ Problems with Random Coefficients 非零端点无限视界FBSDEs的适定性与随机系数LQ问题
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-04-27 DOI: 10.1007/s00245-025-10263-5
Jinghua Li, Zhiyong Yu
{"title":"Well-Posedness of Infinite Horizon FBSDEs with Non-zero Terminals and LQ Problems with Random Coefficients","authors":"Jinghua Li,&nbsp;Zhiyong Yu","doi":"10.1007/s00245-025-10263-5","DOIUrl":"10.1007/s00245-025-10263-5","url":null,"abstract":"<div><p>This paper is concerned with fully coupled forward–backward stochastic differential equations (FBSDEs, for short) with non-zero terminals in infinite horizon. By introducing stochastic Lipschitz conditions and constructing infinite horizon domination–monotonicity conditions, the well-posedness of this kind of infinite horizon FBSDEs including the existence, uniqueness and a pair of estimates is proved. Moreover, the theoretical results are applied to solve four kinds of linear-quadratic (LQ, for short) stochastic optimal control problems with random coefficients in infinite horizon. Due to the unboundedness and randomness of coefficients, the results of the FBSDEs and LQ problems obtained in this paper, even if they are degenerated to finite horizon, contain more situations than the results in the literature.</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":"143879519","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
Lipschitz Multivalued Perturbations of Integro-differential Prox-Regular Sweeping Processes 积分-微分拟正则扫描过程的Lipschitz多值摄动
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-04-19 DOI: 10.1007/s00245-025-10258-2
Tahar Haddad, Sarra Gaouir, Lionel Thibault
{"title":"Lipschitz Multivalued Perturbations of Integro-differential Prox-Regular Sweeping Processes","authors":"Tahar Haddad,&nbsp;Sarra Gaouir,&nbsp;Lionel Thibault","doi":"10.1007/s00245-025-10258-2","DOIUrl":"10.1007/s00245-025-10258-2","url":null,"abstract":"<div><p>Integro-differential sweeping processes with prox-regular sets in Hilbert spaces have been the subject of various recent studies. Diverse applications of such differential inclusions to complementarity problems, electrical circuits, frictionless contact, can be found in the literature. Here we provide a general theorem of existence of solution for such processes perturbed by a Lipschitz multimapping with nonconvex values.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143850899","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
Determination of Singular Control in the Optimal Management of Natural Resources 自然资源最优管理中奇异控制的确定
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-04-12 DOI: 10.1007/s00245-025-10257-3
Chris Guiver, Mark R. Opmeer
{"title":"Determination of Singular Control in the Optimal Management of Natural Resources","authors":"Chris Guiver,&nbsp;Mark R. Opmeer","doi":"10.1007/s00245-025-10257-3","DOIUrl":"10.1007/s00245-025-10257-3","url":null,"abstract":"<div><p>A method is presented to simplify the determination of solutions of certain optimal control problems which commonly arise in natural resource management and bioeconomic contexts. The method, termed the resource-value balance method, essentially leverages an equivalent formulation of the original optimal control problem and, as described, in certain cases the method obviates the need for classical tools from optimal control theory, such as the Pontryagin Principle. Indeed, in these cases the method reduces the original problem to one solvable with elementary calculus techniques. Further, the solution provided by the resource-value balance method is shown to equal the singular solution of an associated (and more commonly considered) input-constrained optimal control problem, providing insight into the nature of singular control in this context. The theory is illustrated with examples from bioeconomics.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10257-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143821770","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
Arched Beams of Bresse Type: Thermoelastic Modeling and Stability Analysis Bresse型拱梁：热弹性建模与稳定性分析
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-04-12 DOI: 10.1007/s00245-025-10255-5
G. E. Bittencourt Moraes, M. A. Jorge Silva
{"title":"Arched Beams of Bresse Type: Thermoelastic Modeling and Stability Analysis","authors":"G. E. Bittencourt Moraes,&nbsp;M. A. Jorge Silva","doi":"10.1007/s00245-025-10255-5","DOIUrl":"10.1007/s00245-025-10255-5","url":null,"abstract":"<div><p>This is the third and final work in a series dedicated to thermoelastic arched beams of Bresse type under Fourier’s law. Herein, our first main goal is to provide a detailed modeling of the thermoelastic Bresse–Fourier systems, addressing thermal couplings and their effects on axial, shear, and bending forces. Then, the stability results are rigorously analyzed, by proving that stability patterns remain consistent under different boundary conditions and thermal couplings. Theoretical contributions include semi-uniform algebraic and uniform exponential decay rates, achieved using semigroup theory. This paper concludes the trilogy by unifying the stability analysis for all remaining systems with new thermal couplings.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143821774","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
Non-asymptotic Convergence Rates for Mean-Field Games: Weak Formulation and McKean–Vlasov BSDEs 平均场对策的非渐近收敛率：弱公式和McKean-Vlasov BSDEs
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-04-11 DOI: 10.1007/s00245-025-10256-4
Dylan Possamaï, Ludovic Tangpi
{"title":"Non-asymptotic Convergence Rates for Mean-Field Games: Weak Formulation and McKean–Vlasov BSDEs","authors":"Dylan Possamaï,&nbsp;Ludovic Tangpi","doi":"10.1007/s00245-025-10256-4","DOIUrl":"10.1007/s00245-025-10256-4","url":null,"abstract":"<div><p>This work is mainly concerned with the so-called limit theory for mean-field games. Adopting the weak formulation paradigm put forward by Carmona and Lacker (Ann Appl Probab 25(3):1189–1231, 2015), we consider a fully non-Markovian setting allowing for drift control and interactions through the joint distribution of players’ states and controls. We provide first a characterisation of mean-field equilibria as arising from solutions to a novel kind of McKean–Vlasov backward stochastic differential equations, for which we provide a well-posedness theory. We incidentally obtain there unusual existence and uniqueness results for mean-field equilibria, which do not require short-time horizon, separability assumptions on the coefficients, nor Lasry and Lions’s monotonicity conditions, but rather smallness—or alternatively regularity—conditions on the terminal reward and a dissipativity condition on the drift. We then take advantage of this characterisation to provide non-asymptotic rates of convergence for the value functions and the Nash-equilibria of the <i>N</i>-player version to their mean-field counterparts, for general open-loop equilibria. An appropriate reformulation of our approach also allows us to treat closed-loop equilibria, and to obtain convergence results for the master equation associated to the problem.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10256-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818246","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
Invariant Sample Measures for Non-autonomous Stochastic Non-local Discrete p-Laplacian Equations with Time Varying Delay and Multiplicative Noises 具有时变延迟和乘法噪声的非自治随机非局部离散 p-Laplacian 方程的不变抽样量纲
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-04-05 DOI: 10.1007/s00245-025-10254-6
Wenqiang Zhao, Xia Liu
{"title":"Invariant Sample Measures for Non-autonomous Stochastic Non-local Discrete p-Laplacian Equations with Time Varying Delay and Multiplicative Noises","authors":"Wenqiang Zhao,&nbsp;Xia Liu","doi":"10.1007/s00245-025-10254-6","DOIUrl":"10.1007/s00245-025-10254-6","url":null,"abstract":"<div><p>In this article, a class of <i>non-local</i> stochastic lattice models with fractional powers of the discrete <i>p</i>-Laplacian, incorporating time-varying-distributed delay as well as multiplicative noises at each node, are propounded. First, by utilizing an existence theorem of solutions for infinite ordinary differential equations, we prove the well-posedness of the stochastic equations, whose solution operator admits an NRDS. Besides, the tempered random attractor is constructed for this NRDS. Finally, with the identical conditions, we prove that the solution is jointly continuous in initial time and initial data, and eventually, a family of invariant sample Borel probability measures supported in the random attractors are established in a Banach space (not a Hilbert space) for the corresponding NRDS.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143778001","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
Analysis of Subdifferentials of Marginal and Performance Functions 边际函数和性能函数的次微分分析
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-04-02 DOI: 10.1007/s00245-025-10251-9
Duong Thi Viet An, Jean-Paul Penot
{"title":"Analysis of Subdifferentials of Marginal and Performance Functions","authors":"Duong Thi Viet An,&nbsp;Jean-Paul Penot","doi":"10.1007/s00245-025-10251-9","DOIUrl":"10.1007/s00245-025-10251-9","url":null,"abstract":"<div><p>We study generalized derivatives of value functions for optimization problems depending on a parameter <i>w</i>. Interpretations of the results obtained with these substitutes to derivatives are known to be important. We endeavour to answer the question: can one obtain these results without knowing the nature of these substitutes and their constructions? Is there a means to obtain them in a unified way?</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761693","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
On the Well-Posedness and Long Time Dynamics for a Coupled Nonlinear Bridge System with Past History 论具有过去历史的耦合非线性桥梁系统的拟合优度和长时动力学
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2025-04-02 DOI: 10.1007/s00245-025-10252-8
Soh Edwin Mukiawa, Salim A. Messaoudi
{"title":"On the Well-Posedness and Long Time Dynamics for a Coupled Nonlinear Bridge System with Past History","authors":"Soh Edwin Mukiawa,&nbsp;Salim A. Messaoudi","doi":"10.1007/s00245-025-10252-8","DOIUrl":"10.1007/s00245-025-10252-8","url":null,"abstract":"<div><p>This work is concerned with a coupled nonlinear mathematical model for a suspension bridge with past history. The vibrations of both the road bed in the vertical plain and main cable from which the road bed is suspended by the tie cables are taken into consideration. Using the semi-group approach, we give a thorough and careful existence and uniqueness result. Also, we prove that the associated solution semi-group has a compact global attractor in an appropriate Hilbert space.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761692","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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