共查询到20条相似文献,搜索用时 78 毫秒
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距离平方函数是最优传输问题中最重要的成本函数之一,它在许多领域都有着重要的应用.本文简要介绍在该成本函数下的最优传输问题,包括解的存在性、正则性、部分正则性以及相关的自由边界问题. 相似文献
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得到了一类变形的传输不等式,给出了判断其是否成立的充分条件和必要条件,并且利用这类不等式,对于指数阶矩不存在的概率测度,建立了相应的多项式型的聚集不等式. 相似文献
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最优保存遗传算法在最优资产事计算中的应用 总被引:1,自引:0,他引:1
本基献[1]的思路,详细论述了利用遗传算法解决有风险控制的最优资产组合问题的具体实现过程。并讨论了用浮点数的方法表示的最优保存遗传算法的全局收敛性。 相似文献
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本文根据宏观经济行为和微观经济行为的辩证关系,设计了一类数学模型,并利用该模型研究了国民经济按比例最优增长及其实现问题.基于模型的分析表明.只要政府调控合适,国民经济就能够按比例最优增长. 相似文献
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本文基文献 [1]的思路 ,详细论述了利用遗传算法解决有风险控制的最优资产组合问题的具体实现过程 .并论证了用浮点数的方法表示的最优保存遗传算法的全局收敛性 相似文献
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偏微分方程在图像去噪中的应用 总被引:15,自引:0,他引:15
本文介绍用于图像去噪的偏微分模型、方法的发展历程.从理论上分析了线性模型、简单非线性模型、复杂非线性模型、多步处理模型出现的背景和优缺点,并从空域和频域上对偏微分方程模型的去噪原理进行了分析.最后,指出了偏微分方程去噪与小波去噪结合的途径,据此对偏微分方程未来的发展方向进行了展望. 相似文献
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姜启源 《数学建模及其应用》2016,5(1):28-42
介绍动物觅食行为的建模。首先考察觅食动物的搜寻、处理所需时间和能量等基本因素如何影响食饵的选择,建立一个初等模型,使觅食动物的净能量获取率最大,并可预测动物的"最优"食物,然后考虑食饵识别时间、食物地块和觅食中心位置等因素来修正、改进这个模型。最后,用一些实验数据来解释这些模型。 相似文献
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姜启源 《数学建模及其应用》2016,4(2)
介绍动物觅食行为的建模。首先考察觅食动物的搜寻、处理所需时间和能量等基本因素如何影响食饵的选择,建立一个初等模型,使觅食动物的净能量获取率最大,并可预测动物的“最优”食物,然后考虑食饵识别时间、食物地块和觅食中心位置等因素来修正、改进这个模型。最后,用一些实验数据来解释这些模型。 相似文献
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G. Bouchitté C. Jimenez M. Rajesh 《Proceedings of the American Mathematical Society》2007,135(11):3525-3535
Let be a bounded Lipschitz regular open subset of and let be two probablity measures on . It is well known that if is absolutely continuous, then there exists, for every , a unique transport map pushing forward on and which realizes the Monge-Kantorovich distance . In this paper, we establish an bound for the displacement map which depends only on , on the shape of and on the essential infimum of the density .
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Martingale optimal transport has attracted much attention due to its application in pricing and hedging in mathematical finance. The essential notion which makes martingale optimal transport different from optimal transport is peacock. A peacock is a sequence of measures which satisfies convex order property. In this paper we study peacock geodesics in Wasserstain space, and we hope this paper can provide some geometrical points of view to look at martingale optimal transport. 相似文献
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Luis A. Caffarelli Mikhail Feldman Robert J. McCann 《Journal of the American Mathematical Society》2002,15(1):1-26
Given two densities on with the same total mass, the Monge transport problem is to find a Borel map rearranging the first distribution of mass onto the second, while minimizing the average distance transported. Here distance is measured by a norm with a uniformly smooth and convex unit ball. This paper gives a complete proof of the existence of optimal maps under the technical hypothesis that the distributions of mass be compactly supported. The maps are not generally unique. The approach developed here is new, and based on a geometrical change-of-variables technique offering considerably more flexibility than existing approaches.
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Lénaïc Chizat Gabriel Peyré Bernhard Schmitzer François-Xavier Vialard 《Journal of Functional Analysis》2018,274(11):3090-3123
This article presents a new class of distances between arbitrary nonnegative Radon measures inspired by optimal transport. These distances are defined by two equivalent alternative formulations: (i) a dynamic formulation defining the distance as a geodesic distance over the space of measures (ii) a static “Kantorovich” formulation where the distance is the minimum of an optimization problem over pairs of couplings describing the transfer (transport, creation and destruction) of mass between two measures. Both formulations are convex optimization problems, and the ability to switch from one to the other depending on the targeted application is a crucial property of our models. Of particular interest is the Wasserstein–Fisher–Rao metric recently introduced independently by [7], [15]. Defined initially through a dynamic formulation, it belongs to this class of metrics and hence automatically benefits from a static Kantorovich formulation. 相似文献
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《Journal of Functional Analysis》2023,284(1):109732
We prove the existence of global minimizers to the double minimization problem where denotes the perimeter of the set E, is the p-Wasserstein distance between Borel probability measures, and is arbitrary. The result holds in all space dimensions, for all , and for all positive λ. This answers a question of Buttazzo, Carlier, and Laborde. 相似文献
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《Stochastic Processes and their Applications》2020,130(9):5575-5591
To quantify the difference of distinct stochastic processes it is not sufficient to consider the distance of their states and corresponding probabilities. Instead, the information, which evolves and accumulates over time and which is mathematically encoded by filtrations, has to be accounted for as well. The nested distance, also known as bicausal Wasserstein distance, recognizes this component and involves the filtration properly. This distance is of emerging importance due to its applications in stochastic analysis, stochastic programming, mathematical economics and other disciplines.This paper investigates the basic metric and topological properties of the nested distance on the space of discrete-time processes. In particular we prove that the nested distance generates a Polish topology, although the genuine space is not complete. Moreover we identify its completion to be the space of nested distributions, a space of generalized stochastic processes. 相似文献
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Mohamed Alahyane Abdelilah Hakim Amine Laghrib Said Raghay 《Mathematical Methods in the Applied Sciences》2019,42(18):7059-7075
In this paper, we present a fast algorithm of the nonparametric elastic image registration using a simple implementation of the Range Restricted GMRES (RRGMRES) method. This approach differs from the others in the fact that it is specified to the tridiagonal block matrix type to resolve a nonsymmetric linear system. In what follows, we prove existence and uniqueness of minimizer of the elastic registration problem and present the corresponding discrete problem by employing a finite difference scheme. The accuracy of the proposed method is demonstrated on different image registration examples; we also show the speedup of the proposed approach by calculating the corresponding CPU time and compared it with the classical elastic registration method. 相似文献
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Let G be a compact Lie group, and consider the loop group LeG:={?∈C([0,1],G); ?(0)=?(1)=e}. Let ν be the heat kernel measure at the time 1. For any density function F on LeG such that Entν(F)<∞, we shall prove that there exists a unique optimal transportation map which pushes ν forward to Fν. 相似文献
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In stochastic optimization models, the optimal solution heavily depends on the selected probability model for the scenarios. However, the scenario models are typically chosen on the basis of statistical estimates and are therefore subject to model error. We demonstrate here how the model uncertainty can be incorporated into the decision making process. We use a nonparametric approach for quantifying the model uncertainty and a minimax setup to find model-robust solutions. The method is illustrated by a risk management problem involving the optimal design of an insurance contract. 相似文献