Regularity properties of the Schrödinger cost.

IF 1.3 3区数学 Q4 AUTOMATION & CONTROL SYSTEMS

Esaim-Control Optimisation and Calculus of Variations Pub Date : 2022-04-22 DOI:10.1051/cocv/2022033

Gauthier Clerc

引用次数: 0

Abstract

The Schrödinger problem is an entropy minimisation problem on the space of probability measures. Its optimal value is a cost between two probability measures. In this article we investigate some regularity properties of this cost: continuity with respect to the marginals and time derivative of the cost along probability measures valued curves.

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Schrödinger成本的正则性。

Schrödinger问题是概率测度空间上的熵最小化问题。它的最优值是两个概率测度之间的代价。在本文中，我们研究了这种代价的一些正则性:关于边际的连续性和代价沿概率测度值曲线的时间导数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Esaim-Control Optimisation and Calculus of Variations Mathematics-Computational Mathematics

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7.10%

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期刊介绍： ESAIM: COCV strives to publish rapidly and efficiently papers and surveys in the areas of Control, Optimisation and Calculus of Variations. Articles may be theoretical, computational, or both, and they will cover contemporary subjects with impact in forefront technology, biosciences, materials science, computer vision, continuum physics, decision sciences and other allied disciplines. Targeted topics include: in control: modeling, controllability, optimal control, stabilization, control design, hybrid control, robustness analysis, numerical and computational methods for control, stochastic or deterministic, continuous or discrete control systems, finite-dimensional or infinite-dimensional control systems, geometric control, quantum control, game theory; in optimisation: mathematical programming, large scale systems, stochastic optimisation, combinatorial optimisation, shape optimisation, convex or nonsmooth optimisation, inverse problems, interior point methods, duality methods, numerical methods, convergence and complexity, global optimisation, optimisation and dynamical systems, optimal transport, machine learning, image or signal analysis; in calculus of variations: variational methods for differential equations and Hamiltonian systems, variational inequalities; semicontinuity and convergence, existence and regularity of minimizers and critical points of functionals, relaxation; geometric problems and the use and development of geometric measure theory tools; problems involving randomness; viscosity solutions; numerical methods; homogenization, multiscale and singular perturbation problems.