Applied Mathematics and Optimization最新文献_第8页

Bilevel Optimization of the Kantorovich Problem and Its Quadratic Regularization 康托洛维奇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 : 2024-07-14 DOI: 10.1007/s00245-024-10162-1

Sebastian Hillbrecht, Paul Manns, Christian Meyer

{"title":"Bilevel Optimization of the Kantorovich Problem and Its Quadratic Regularization","authors":"Sebastian Hillbrecht, Paul Manns, Christian Meyer","doi":"10.1007/s00245-024-10162-1","DOIUrl":"10.1007/s00245-024-10162-1","url":null,"abstract":"<div>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 second part in a series of three papers. While the existence of optimal solutions to both the bilevel Kantorovich problem and its regularized counterpart were shown in the first part, this paper deals with the (weak-(*)) convergence of solutions to the regularized bilevel problem to solutions of the original bilevel Kantorovich problem for vanishing regularization parameters.</div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"90 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-024-10162-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141649856","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

Moderate Deviations for Two-Time Scale Systems with Mixed Fractional Brownian Motion 具有混合分数布朗运动的两时间尺度系统的适度偏差

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-07-08 DOI: 10.1007/s00245-024-10159-w

Xiaoyu Yang, Yuzuru Inahama, Yong Xu

引用次数: 0

Nonuniqueness of Weak Solutions to the Dissipative Aw–Rascle Model 耗散 Aw-Rascle 模型弱解的非唯一性

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-07-08 DOI: 10.1007/s00245-024-10158-x

Nilasis Chaudhuri, Eduard Feireisl, Ewelina Zatorska

引用次数: 0

A Nesterov Type Algorithm with Double Tikhonov Regularization: Fast Convergence of the Function Values and Strong Convergence to the Minimal Norm Solution 具有双重 Tikhonov 正则化的涅斯捷罗夫型算法：函数值的快速收敛和向最小规范解的强收敛

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-07-05 DOI: 10.1007/s00245-024-10163-0

Mikhail Karapetyants, Szilárd Csaba László

引用次数: 0

Upper Semicontinuity of Random Attractors for Random Differential Equations with Nonlinear Diffusion Terms I: Finite-Dimensional Case 带有非线性扩散项的随机微分方程的随机吸引子的上半连续性 I：有限维情况

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-07-04 DOI: 10.1007/s00245-024-10164-z

Anhui Gu

引用次数: 0

Nonlocal Green Theorems and Helmholtz Decompositions for Truncated Fractional Gradients 截断分数梯度的非局部格林定理和亥姆霍兹分解

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-07-04 DOI: 10.1007/s00245-024-10160-3

José Carlos Bellido, Javier Cueto, Mikil D. Foss, Petronela Radu

引用次数: 0

Integer Optimal Control with Fractional Perimeter Regularization 带分数周边正则化的整数优化控制

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-07-01 DOI: 10.1007/s00245-024-10157-y

Harbir Antil, Paul Manns

{"title":"Integer Optimal Control with Fractional Perimeter Regularization","authors":"Harbir Antil, Paul Manns","doi":"10.1007/s00245-024-10157-y","DOIUrl":"10.1007/s00245-024-10157-y","url":null,"abstract":"<div>Motivated by many applications, optimal control problems with integer controls have recently received a significant attention. Some state-of-the-art work uses perimeter-regularization to derive stationarity conditions and trust-region algorithms. However, the discretization is difficult in this case because the perimeter is concentrated on a set of dimension (d - 1) for a domain of dimension d. This article proposes a potential way to overcome this challenge by using the fractional nonlocal perimeter with fractional exponent (0<alpha <1). In this way, the boundary integrals in the perimeter regularization are replaced by volume integrals. Besides establishing some non-trivial properties associated with this perimeter, a (Gamma )-convergence result is derived. This result establishes convergence of minimizers of fractional perimeter-regularized problem, to the standard one, as the exponent (alpha ) tends to 1. In addition, the stationarity results are derived and algorithmic convergence analysis is carried out for (alpha in (0.5,1)) under an additional assumption on the gradient of the reduced objective. The theoretical results are supplemented by a preliminary computational experiment. We observe that the isotropy of the total variation may be approximated by means of the fractional perimeter functional.\u0000</div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"90 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-024-10157-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141523666","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

Multiple Positive Solutions for Quasilinear Elliptic Problems in Expanding Domains 扩展域中准线性椭圆问题的多重正解

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-06-29 DOI: 10.1007/s00245-024-10155-0

Wulong Liu, Guowei Dai, Patrick Winkert, Shengda Zeng

引用次数: 0

Continuous-Time Mean Field Markov Decision Models 连续时间均值场马尔可夫决策模型

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-06-22 DOI: 10.1007/s00245-024-10154-1

Nicole Bäuerle, Sebastian Höfer

{"title":"Continuous-Time Mean Field Markov Decision Models","authors":"Nicole Bäuerle, Sebastian Höfer","doi":"10.1007/s00245-024-10154-1","DOIUrl":"10.1007/s00245-024-10154-1","url":null,"abstract":"<div>We consider a finite number of N statistically equal agents, each moving on a finite set of states according to a continuous-time Markov Decision Process (MDP). Transition intensities of the agents and generated rewards depend not only on the state and action of the agent itself, but also on the states of the other agents as well as the chosen action. Interactions like this are typical for a wide range of models in e.g. biology, epidemics, finance, social science and queueing systems among others. The aim is to maximize the expected discounted reward of the system, i.e. the agents have to cooperate as a team. Computationally this is a difficult task when N is large. Thus, we consider the limit for (Nrightarrow infty .) In contrast to other papers we treat this problem from an MDP perspective. This has the advantage that we need less regularity assumptions in order to construct asymptotically optimal strategies than using viscosity solutions of HJB equations. The convergence rate is (1/sqrt{N}). We show how to apply our results using two examples: a machine replacement problem and a problem from epidemics. We also show that optimal feedback policies from the limiting problem are not necessarily asymptotically optimal.</div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"90 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00245-024-10154-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413115","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

Global Behavior in a Two-Species Chemotaxis-Competition System with Signal-Dependent Sensitivities and Nonlinear Productions 具有信号敏感性和非线性产物的双物种趋化竞争系统的全局行为

IF 1.6 2区数学

Applied Mathematics and Optimization Pub Date : 2024-06-22 DOI: 10.1007/s00245-024-10137-2

Zhan Jiao, Irena Jadlovská, Tongxing Li

{"title":"Global Behavior in a Two-Species Chemotaxis-Competition System with Signal-Dependent Sensitivities and Nonlinear Productions","authors":"Zhan Jiao, Irena Jadlovská, Tongxing Li","doi":"10.1007/s00245-024-10137-2","DOIUrl":"10.1007/s00245-024-10137-2","url":null,"abstract":"<div>This article considers a two competitive biological species system involving signal-dependent motilities and sensitivities and nonlinear productions <div><div>$$begin{aligned} left{ begin{array}{l} begin{aligned} &{}u_t = nabla cdot big (D_1(v)nabla u-uS_1(v)nabla vbig )+mu _1u(1-u^{alpha _1}-a_1w),&{} xin Omega , t>0&{}, &{} v_t=Delta v-v+b_1w^{gamma _1}, &{} xin Omega , t>0&{}, &{}w_t = nabla cdot big (D_2(z)nabla w-wS_2(z)nabla zbig )+mu _2w(1-w^{alpha _2}-a_2u),&{} xin Omega , t>0&{}, &{} z_t=Delta z-z+b_2u^{gamma _2}, &{} xin Omega , t>0&{} end{aligned} end{array} right. end{aligned}$$</div></div>in a bounded and smooth domain (Omega subset mathbb R^2), where the parameters (mu _i, alpha _i, a_i, b_i, gamma _i) ((i=1,2)) are positive constants, and the functions (D_1(v),S_1(v),D_2(z),S_2(z)) fulfill the following hypotheses: (Diamond ) (D_i(psi ),S_i(psi )in C^2([0,infty ))), (D_i(psi ),S_i(psi )>0) for all (psi ge 0), (D_i^{prime }(psi )<0) and (underset{psi rightarrow infty }{lim } D_i(psi )=0); (Diamond ) (underset{psi rightarrow infty }{lim } frac{S_i(psi )}{D_i(psi )}) and (underset{psi rightarrow infty }{lim } frac{D^{prime }_i(psi )}{D_i(psi )}) exist. We first confirm the global boundedness of the classical solution provided that the additional conditions (2gamma _1le 1+alpha _2) and (2gamma _2le 1+alpha _1) hold. Moreover, by constructing several suitable Lyapunov functionals, it is demonstrated that the global solution exponentially or algebraically converges to the constant stationary solutions and the corresponding convergence rates are determined under some specific stress conditions.\u0000</div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"90 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413102","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