Q1. What are the contributions in "A curse-of-dimensionality-free numerical method for a class of hjb pde’s" ?
Here the authors consider HJB PDEs where the Hamiltonian takes the form of a ( pointwise ) maximum of linear/quadratic forms.
A curse-of-dimensionality-free numerical method for a class of HJB PDE's
TLDR
In this article, the authors consider HJB PDEs where the Hamiltonian takes the form of a (pointwise) maximum of linear/quadratic forms and obtain a numerical method not subject to the curse of dimensionality.About:
This article is published in IFAC Proceedings Volumes.The article was published on 2005-01-01 and is currently open access. It has received 4 citations till now. The article focuses on the topics: Semigroup & Hamilton–Jacobi–Bellman equation.read more
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Journal ArticleDOI
Stochastic optimal control via forward and backward stochastic differential equations and importance sampling
TL;DR: This scheme is shown to be capable of learning the optimal control without requiring an initial guess and to enhance the efficiency of the proposed scheme when treating more complex nonlinear systems, an iterative algorithm based on Girsanov's theorem on the change of measure is derived.
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A new fundamental solution for differential Riccati equations arising in control
TL;DR: In this article, the authors considered the matrix differential Riccati equation (DRE) as a finite-dimensional solution to a deterministic linear/quadratic control problem and proposed a semiconvex dual of the associated semigroup.
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Convergence Rate for a Curse-of-Dimensionality-Free Method for a Class of HJB PDEs
TL;DR: This work obtains specific error bounds for a previously obtained numerical method not subject to the curse-of-dimensionality of HJB PDEs where the Hamiltonian takes the form of a (pointwise) maximum of linear/quadratic forms.
Proceedings ArticleDOI
Idempotent method for dynamic games and complexity reduction in min-max expansions
TL;DR: It is shown that a similar, albeit more abstract, approach can be applied to deterministic game problems by finding reduced-complexity approximations to min-max sums of max-plus affine functions.
References
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Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations
TL;DR: In this paper, the main ideas on a model problem with continuous viscosity solutions of Hamilton-Jacobi equations are discussed. But the main idea of the main solutions is not discussed.
Journal ArticleDOI
Using randomization to break the curse of dimensionality
TL;DR: In this paper, random versions of successive approximations and multigrid algorithms for computing approximate solutions to a class of finite and infinite horizon Markovian decision problems (MDPs) were introduced.
Book
Idempotent Analysis and Its Applications
TL;DR: In this article, a generalized solution of Bellman's Differential Equation and multiplicative additive asymptotics is presented, which is based on the Maslov Optimziation Theory.
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Duality and separation theorems in idempotent semimodules
TL;DR: In this article, a nonlinear projection on subsemimodules is introduced, where the projection of a point is the maximal approximation from below of the point in the sub-semimmodule.
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Idempotent functional analysis: An algebraic approach
TL;DR: In this paper, an algebraic approach to idempotent functional analysis is presented, which is an abstract version of the traditional functional analysis developed by V. P. Maslov and his collaborators.