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The Regulator Problem for the Wave Equation with High Internal Damping Controlled on the Boundary: A New Look via Systems with Memory 边界上高内阻尼波动方程的调节器问题：基于记忆系统的新视角
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2026-05-07 DOI: 10.1007/s00245-026-10424-0
Luciano Pandolfi
{"title":"The Regulator Problem for the Wave Equation with High Internal Damping Controlled on the Boundary: A New Look via Systems with Memory","authors":"Luciano Pandolfi","doi":"10.1007/s00245-026-10424-0","DOIUrl":"10.1007/s00245-026-10424-0","url":null,"abstract":"<div><p>We study the quadratic regulator problem on a finite time horizon for the wave equation with high internal damping controlled on the boundary by square integrable controls. The approach in this paper transforms the wave equation with high internal damping to an equation with persistent memory controlled on the boundary. One of the results of this paper is the introduction of a state space which is an extended Hilbert space, so a time dependent Hilbert space. We prove that the unique optimal control can be represented as a feedback control via a Riccati operator which solves a suitable version of the Riccati equation. Both the feedback operator and the Riccati equation act on such time dependent space. The derivation of these main results requires a very precise analysis of the properties of the derivatives of the value function and we find an explicit form for the derivative of the Riccati operator.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"93 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829418","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
Large Deviations and Optimal Control for Markov Decision Processes 马尔可夫决策过程的大偏差与最优控制
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2026-05-06 DOI: 10.1007/s00245-026-10446-8
Xiaoyang Lu, Jinwen Chen
{"title":"Large Deviations and Optimal Control for Markov Decision Processes","authors":"Xiaoyang Lu,&nbsp;Jinwen Chen","doi":"10.1007/s00245-026-10446-8","DOIUrl":"10.1007/s00245-026-10446-8","url":null,"abstract":"<div><p>This paper investigates large deviation asymptotics for empirical measures of Markov decision processes on compact space. Building on results in risk-sensitive control, we derive a large deviation upper bound for state–action frequencies uniformly over initial states and policies. Zero points of the corresponding rate function are used to characterize accumulation points of empirical measures and their expected values. For the state frequencies, we also obtain a large deviation lower bound, thereby establishing a controlled version of the large deviation principle. Results for the empirical means of rewards are also presented. As an application, we establish the existence of an <span>(epsilon )</span>-optimal randomized stationary policy for a large deviation control problem.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"93 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829395","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
Local-in-Time Well-Posedness for 2D Compressible Magneto-micropolar Boundary Layer Equations in Sobolev Spaces Sobolev空间中二维可压缩磁微极边界层方程的局域时间适定性
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2026-05-06 DOI: 10.1007/s00245-025-10378-9
Yuming Qin, Junchen Liu
{"title":"Local-in-Time Well-Posedness for 2D Compressible Magneto-micropolar Boundary Layer Equations in Sobolev Spaces","authors":"Yuming Qin,&nbsp;Junchen Liu","doi":"10.1007/s00245-025-10378-9","DOIUrl":"10.1007/s00245-025-10378-9","url":null,"abstract":"<div><p>In this paper, we study the two-dimensional compressible magneto-micropolar boundary layer equations on the half-plane, which are derived from 2D compressible magneto-micropolar fluid equations with the non-slip boundary condition on velocity, Dirichlet boundary condition on micro-rotational velocity and perfectly conducting boundary condition on magnetic field. Based on a nonlinear coordinate transformation proposed in [1], we first prove the local-in-time well-posedness for the compressible magneto-micropolar boundary layer system in Sobolev spaces, provided that initial tangential magnetic field is non-degenerate.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"93 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829491","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
Approximations with Performance Bounds for a Class of Average Cost Markov Decision Processes with Weakly Continuous Kernel and Unbounded Cost Function 一类具有弱连续核和无界代价函数的平均代价马尔可夫决策过程的性能界逼近
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2026-05-02 DOI: 10.1007/s00245-026-10440-0
Mauricio Castro-Enríquez, Óscar Vega-Amaya, Fernando Luque-Vásquez
{"title":"Approximations with Performance Bounds for a Class of Average Cost Markov Decision Processes with Weakly Continuous Kernel and Unbounded Cost Function","authors":"Mauricio Castro-Enríquez,&nbsp;Óscar Vega-Amaya,&nbsp;Fernando Luque-Vásquez","doi":"10.1007/s00245-026-10440-0","DOIUrl":"10.1007/s00245-026-10440-0","url":null,"abstract":"<div><p>The present work proposes an approximating scheme to compute approximate solutions for a class of average cost Markov decision processes with unbounded costs and weakly continuous kernel. The approximations rely on function approximating schemes that can be represented as positive linear operators that gives exact representation to the constant functions. This allows to see the approximated model as a perturbation of the original model and to derive performance bounds for the approximate optimal stationary policies among other things. The bounds are given in terms of the primitive data of the model and the accuracy of the function approximating scheme that is used. It is assumed that the model satisfies a growth condition, a contraction property expressed as a Lyapuov condition and some standard continuity/compactness conditions.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"93 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796457","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
Extremal Eigenvalues of Weighted Steklov Problems 加权Steklov问题的极值特征值
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2026-04-30 DOI: 10.1007/s00245-026-10438-8
Chiu-Yen Kao, Seyyed Abbas Mohammadi
{"title":"Extremal Eigenvalues of Weighted Steklov Problems","authors":"Chiu-Yen Kao,&nbsp;Seyyed Abbas Mohammadi","doi":"10.1007/s00245-026-10438-8","DOIUrl":"10.1007/s00245-026-10438-8","url":null,"abstract":"<div><p>We study the optimization of Steklov eigenvalues with respect to a boundary density function <span>(rho )</span> on a bounded Lipschitz domain <span>(Omega subset mathbb {R}^N)</span>. We investigate the minimization and maximization of <span>(lambda _k(rho ))</span>, the <i>k</i>th Steklov eigenvalue, over admissible densities satisfying pointwise bounds and a fixed integral constraint. Our analysis covers both first and higher-order eigenvalues and applies to domains <span>(Omega )</span> with general geometry and topology. We establish the existence of optimal solutions and provide structural characterizations: minimizers are bang--bang functions and may have disconnected support, while maximizers are not necessarily bang--bang. On circular domains, the minimization problem admits infinitely many minimizers generated by rotational symmetry, while the maximization problem has infinitely many distinct maximizers that are not symmetry-induced. We also show that the maps <span>(rho mapsto lambda _k(rho ))</span> and <span>(rho mapsto 1/lambda _k(rho ))</span> are generally neither convex nor concave, limiting the use of classical convex optimization tools. To address these challenges, we analyze the objective functional and introduce a Fréchet differentiable surrogate that enables the derivation of optimality conditions. We further design an efficient numerical algorithm, with experiments illustrating the difficulty of recovering optimal densities when they lack smoothness or exhibit oscillations.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"93 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-026-10438-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147797161","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
Limiting Normal Cone to Quadric Surfaces, Local Uniqueness and Error Bound in M-stationarity 法锥对二次曲面的限制、m -平稳性的局部唯一性和误差界
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2026-04-29 DOI: 10.1007/s00245-026-10441-z
Fabián Flores-Bazán, Filip Thiele, Dinh Hoang Nguyen
{"title":"Limiting Normal Cone to Quadric Surfaces, Local Uniqueness and Error Bound in M-stationarity","authors":"Fabián Flores-Bazán,&nbsp;Filip Thiele,&nbsp;Dinh Hoang Nguyen","doi":"10.1007/s00245-026-10441-z","DOIUrl":"10.1007/s00245-026-10441-z","url":null,"abstract":"<div><p>M-stationarity, which involves the limiting (Mordukhovich or basic) normal cone has proved having various advantages, for instance in comparison with KKT optimality conditions; even if Fritz John optimality condition is considered. We actually show an example of an optimization problem where solutions are localized exclusively via M-stationarity. This paper deals with geometric constraint sets (named quadric surfaces or simply quadric) that are determined by a quadratic function, and presents a formula for the limiting normal cone, which is not necessarily the union of polyhedra, to the union of two quadric surfaces. Afterwards, we establish local uniqueness and sensitivity results in nonconvex quadratic programming in the context of M-stationarity.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"93 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796949","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
Inertial Accelerated Primal–Dual Algorithms for Non-smooth Convex Optimization Problems with Linear Equality Constraints 线性等式约束下非光滑凸优化问题的惯性加速原对偶算法
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2026-04-28 DOI: 10.1007/s00245-026-10442-y
Huan Zhang, Xiangkai Sun, Shengjie Li, Kok Lay Teo
{"title":"Inertial Accelerated Primal–Dual Algorithms for Non-smooth Convex Optimization Problems with Linear Equality Constraints","authors":"Huan Zhang,&nbsp;Xiangkai Sun,&nbsp;Shengjie Li,&nbsp;Kok Lay Teo","doi":"10.1007/s00245-026-10442-y","DOIUrl":"10.1007/s00245-026-10442-y","url":null,"abstract":"<div><p>This paper is devoted to the study\u0000 of an inertial accelerated primal–dual algorithm, which is based on a second-order differential system with time scaling, for solving a non-smooth convex optimization problem with linear equality constraints. We first introduce a second-order differential system with time scaling associated with the non-smooth convex optimization problem, and then obtain fast convergence rates for the primal–dual gap, the feasibility violation, and the objective residual along the trajectory generated by this system. Subsequently, based on the setting of the parameters involved, we propose an inertial accelerated primal–dual algorithm from the time discretization of this system. We also establish fast convergence rates for the primal–dual gap, the feasibility violation, and the objective residual. Furthermore, we demonstrate the efficacy of the proposed algorithm through numerical experiments.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"93 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796569","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 a Shear Thermoelastic Bresse System: Well Posedness and Stability 切变热弹性系统：良好的稳定性
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2026-04-25 DOI: 10.1007/s00245-026-10437-9
Salim A. Messaoudi, Ahmed Keddi, Mohamed Alahyane
{"title":"On a Shear Thermoelastic Bresse System: Well Posedness and Stability","authors":"Salim A. Messaoudi,&nbsp;Ahmed Keddi,&nbsp;Mohamed Alahyane","doi":"10.1007/s00245-026-10437-9","DOIUrl":"10.1007/s00245-026-10437-9","url":null,"abstract":"<div><p>This paper is concerned with a one-dimensional linear truncated thermoelastic Bresse system formed by two hyperbolic equations and one elliptic equation coupled with a heat equation of Fourier type. By exploiting some non classical differential operators, we prove the well posedness, using the semigroup theory. We then show that the system is exponentially stable if and only if the hyperbolic equations have the same speed of wave propogation. In the opposite case, we establish a polynomial decay. Moreover, we illustrate our results through some numerical tests.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"93 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738803","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
Intrinsic Regularization by Noise for 1d Mean Field Games 一维平均场博弈的噪声内禀正则化
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2026-04-21 DOI: 10.1007/s00245-026-10434-y
François Delarue, Youssef Ouknine
{"title":"Intrinsic Regularization by Noise for 1d Mean Field Games","authors":"François Delarue,&nbsp;Youssef Ouknine","doi":"10.1007/s00245-026-10434-y","DOIUrl":"10.1007/s00245-026-10434-y","url":null,"abstract":"<div><p>The purpose of this article is to show that an intrinsic noise with values in the space <span>({mathcal {P}}({mathbb {R}}))</span> of 1<i>d</i> probability measures may force uniqueness to first order mean field games. The structure of the noise is inspired from the earlier work (Delarue and Hammersley in Probab Theory Relat Fields 191(1–2):41–102, 2025) . It reads as a coloured Ornstein-Uhlenbeck process with reflection on the boundary of quantile functions on the 1<i>d</i> torus, with the elements of the latter playing the role of indices for the continuum of players underpinning the game. In Delarue and Hammersley (Probab Theory Relat Fields 191(1–2):41–102, 2025), the semi-group generated by the noise is shown to enjoy smoothing properties that become key in the study carried out here. Although the analysis is limited to the 1d setting, this is the first example of uniqueness forcing for generic mean field games set over an infinite dimensional set of probability measures and this may be one step forward towards a more systematic regularization by noise theory for mean field games.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"93 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738501","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
Efficient Douglas–Rachford Methods on Hadamard Manifolds with Applications to the Heron Problems Hadamard流形上的有效Douglas-Rachford方法及其在Heron问题中的应用
IF 1.7 2区 数学
Applied Mathematics and Optimization Pub Date : 2026-04-20 DOI: 10.1007/s00245-026-10402-6
D. R. Sahu, Shikher Sharma, Pankaj Gautam
{"title":"Efficient Douglas–Rachford Methods on Hadamard Manifolds with Applications to the Heron Problems","authors":"D. R. Sahu,&nbsp;Shikher Sharma,&nbsp;Pankaj Gautam","doi":"10.1007/s00245-026-10402-6","DOIUrl":"10.1007/s00245-026-10402-6","url":null,"abstract":"<div><p>Our interest lies in developing some efficient methods for minimizing the sum of two geodesically convex functions on Hadamard manifolds, with the aim of improving the convergence of the Douglas–Rachford algorithm in Hadamard manifolds. Specifically, we propose two types of algorithms: inertial and non-inertial algorithms. The convergence analysis of both algorithms is provided under suitable assumptions on algorithmic parameters and the geodesic convexity of the objective functions. This convergence analysis is based on fixed-point theory for nonexpansive operators. We also study the convergence rates of these two methods. Additionally, we introduce parallel Douglas–Rachford type algorithms for minimizing functionals containing multiple summands with applications to the generalized Heron problem on Hadamard manifolds. To demonstrate the effectiveness of the proposed algorithms, we present some numerical experiments for the generalized Heron problems.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"93 3","pages":""},"PeriodicalIF":1.7,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-026-10402-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738021","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
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