Applied Mathematics and Optimization最新文献_第5页

Optimal Control of Two-Phase Membrane Problem 两相膜问题的最优控制

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-06-28 DOI: 10.1007/s00245-025-10282-2

Farid Bozorgnia, Vyacheslav Kungurtsev

引用次数: 0

Entire Solutions of Stochastic Unbounded Delay Evolution Variational Inequalities Driven by Tempered Fractional Noise with an Exponential Dichotomy 缓变分数噪声驱动的随机无界延迟演化变分不等式的全解

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-06-28 DOI: 10.1007/s00245-025-10284-0

Gang Cao, Yejuan Wang, Xiaoying Han, Peter E. Kloeden

{"title":"Entire Solutions of Stochastic Unbounded Delay Evolution Variational Inequalities Driven by Tempered Fractional Noise with an Exponential Dichotomy","authors":"Gang Cao, Yejuan Wang, Xiaoying Han, Peter E. Kloeden","doi":"10.1007/s00245-025-10284-0","DOIUrl":"10.1007/s00245-025-10284-0","url":null,"abstract":"<div>The aim of this paper is to study a stochastic unbounded delay evolution variational inequality which consists of a stochastic unbounded delay evolution equation driven by tempered fractional noise with exponential dichotomy and a stochastic variational inequality. First, the existence and uniqueness of the mild solution on ( {mathbb {R}} ) are established for the linear stochastic evolution equation overcoming the challenges posed by the exponential dichotomy of the evolution family ( left{ S(t,s)right} _{tge s} ) generated by the family of closed, densely defined linear operators A(t) in (1). Then after giving the equivalent form of the stochastic variational inequality defined on ( {mathbb {R}} ), the existence and uniqueness of the mild solution on ( {mathbb {R}} ) are proved for the stochastic unbounded delay evolution variational inequality (1) by using the Banach fixed point theorem instead of the iteration method and convergence analysis. Notably, due to the nontrivial exponential dichotomy of the evolution family ( left{ S(t,s)right} _{tge s} ), the stability can not be established for the nonlinear stochastic evolution variational inequality (1) and even for the linear stochastic evolution equation (5). Moreover, we show the exponential stability of the nontrivial equilibrium solution for the stochastic unbounded delay evolution variational inequality (1) but under the assumption that the evolution family ( left{ S(t,s)right} _{tge s} ) is exponential stable. Finally, the stochastic reaction diffusion variational inequality is considered as an example of application.</div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170455","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 Approximations for Mean-Field Type Multi-agent Control and Their Near Optimality 平均场型多智能体控制的有限逼近及其近最优性

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-06-27 DOI: 10.1007/s00245-025-10279-x

Erhan Bayraktar, Nicole Bäuerle, Ali Devran Kara

{"title":"Finite Approximations for Mean-Field Type Multi-agent Control and Their Near Optimality","authors":"Erhan Bayraktar, Nicole Bäuerle, Ali Devran Kara","doi":"10.1007/s00245-025-10279-x","DOIUrl":"10.1007/s00245-025-10279-x","url":null,"abstract":"<div>We study a multi-agent mean-field type control problem in discrete time where the agents aim to find a socially optimal strategy and where the state and action spaces for the agents are assumed to be continuous. The agents are only weakly coupled through the distribution of their state variables. The problem in its original form can be formulated as a classical Markov decision process (MDP), however, this formulation suffers from several practical difficulties. In this work, we attempt to overcome the curse of dimensionality, coordination complexity between the agents, and the necessity of perfect feedback collection from all the agents (which might be hard to do for large populations.) We provide several approximations: we establish the near optimality of the action and state space discretization of the agents under standard regularity assumptions for the considered formulation by constructing and studying the measure valued MDP counterpart for finite and infinite population settings. It is a well known approach to consider the infinite population problem for mean-field type models, since it provides symmetric policies for the agents which simplifies the coordination between the agents. However, the optimality analysis is harder as the state space of the measure valued infinite population MDP is continuous (even after space discretization of the agents). Therefore, as a final step, we provide two further approximations for the infinite population problem: the first one directly aggregates the probability measure space, and requires the distribution of the agents to be collected and mapped with a nearest neighbor map, and the second method approximates the measure valued MDP through the empirical distributions of a smaller sized sub-population, for which one only needs keep track of the mean-field term as an estimate by collecting the state information of a small sub-population. For each of the approximation methods, we provide provable regret bounds.</div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170661","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

Anisotropic Double Phase Elliptic Inclusion Systems with Logarithmic Perturbation and Multivalued Convections 具有对数扰动和多值对流的各向异性双相椭圆包体系统

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-06-24 DOI: 10.1007/s00245-025-10278-y

Shengda Zeng, Yasi Lu, Vicenţiu D. Rădulescu

引用次数: 0

Discrete Approximations and Optimality Conditions for Integro-Differential Inclusions 积分-微分包含的离散逼近和最优性条件

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-06-24 DOI: 10.1007/s00245-025-10272-4

Abderrahim Bouach, Tahar Haddad, Boris S. Mordukhovich

{"title":"Discrete Approximations and Optimality Conditions for Integro-Differential Inclusions","authors":"Abderrahim Bouach, Tahar Haddad, Boris S. Mordukhovich","doi":"10.1007/s00245-025-10272-4","DOIUrl":"10.1007/s00245-025-10272-4","url":null,"abstract":"<div>This paper addresses a new class of generalized Bolza problems governed by nonconvex integro-differential inclusions with endpoint constraints on trajectories, where the integral terms are given in the general (with time-dependent integrands in the dynamics) Volterra form. We pursue here a threefold goal. First we construct well-posed approximations of continuous-time integro-differential systems by their discrete-time counterparts with showing that any feasible solution to the original system can be strongly approximated in the (W^{1,2})-norm topology by piecewise-linear extensions of feasible discrete trajectories. This allows us to verify in turn the strong convergence of discrete optimal solutions to a prescribed local minimizer for the original problem. Facing intrinsic nonsmoothness of original integro-differential problem and its discrete approximations, we employ appropriate tools of generalized differentiation in variational analysis to derive necessary optimality conditions for discrete-time problems (which is our second goal) and finally accomplish our third goal to obtain necessary conditions for the original continuous-time problems by passing to the limit from discrete approximations. In this way we establish, in particular, a novel necessary optimality condition of the Volterra type, which is the crucial result for dynamic optimization of integro-differential inclusions.</div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168210","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

Hausdorff Dimension of Random Attractors for a Stochastic Delayed Parabolic Equation in Banach Spaces Banach空间中随机延迟抛物方程随机吸引子的Hausdorff维数

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-06-24 DOI: 10.1007/s00245-025-10281-3

Wenjie Hu, Tomás Caraballo, Yueliang Duan

引用次数: 0

Wasserstein Convergence Rate for Empirical Measures of Markov Processes 马尔可夫过程经验测度的Wasserstein收敛率

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-06-24 DOI: 10.1007/s00245-025-10275-1

Feng-Yu Wang

引用次数: 0

On Shape Optimization for Fourth Order Steklov eigenvalue Problems 四阶Steklov特征值问题的形状优化

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-06-20 DOI: 10.1007/s00245-025-10277-z

Changwei Xiong, Jinglong Yang, Jinchao Yu

引用次数: 0

Optimal Control for Coupled Sweeping Processes Under Minimal Assumptions 最小假设下耦合扫瞄过程的最优控制

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-06-17 DOI: 10.1007/s00245-025-10268-0

Samara Chamoun, Vera Zeidan

{"title":"Optimal Control for Coupled Sweeping Processes Under Minimal Assumptions","authors":"Samara Chamoun, Vera Zeidan","doi":"10.1007/s00245-025-10268-0","DOIUrl":"10.1007/s00245-025-10268-0","url":null,"abstract":"<div>In this paper, the study of nonsmooth optimal control problems (P) involving a controlled sweeping process with three main characteristics is launched. First, the sweeping sets are nonsmooth, time-dependent, and uniformly prox-regular. Second, the sweeping process is coupled with a controlled differential equation. Third, a joint-state endpoints constraint set S is present. This general model incorporates different important controlled submodels, such as a class of second order sweeping processes, and coupled evolution variational inequalities. A full form of the nonsmooth Pontryagin maximum principle for strong local minimizers in (P) is derived for bounded or unbounded moving sweeping sets satisfying local constraint qualifications (CQ) without any additional restriction. The existence and uniqueness of a Lipschitz solution for the Cauchy problem of our dynamic is established and the existence of an optimal solution for (P) is obtained. Two of the novelties in achieving the first goal are (i) the construction of a problem over truncated sweeping sets and truncated joint endpoints constraint set that has the same strong local minimizer as (P) and its (CQ) automatically holds, and (ii) the complete redesign of the exponential-penalty approximation technique for problems with moving sweeping sets that do not require any special assumption on the sets, their corners, or on the gradients of their generators. The utility of the optimality conditions is illustrated with an example.</div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"92 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-025-10268-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166459","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

Taming the Interacting Particle Langevin Algorithm: The Superlinear case 驯服相互作用粒子朗格万算法：超线性情况

IF 1.7 2区数学

Applied Mathematics and Optimization Pub Date : 2025-06-13 DOI: 10.1007/s00245-025-10269-z

Tim Johnston, Nikolaos Makras, Sotirios Sabanis

引用次数: 0