Results 151 to 160 of about 702 (187)

Consistency of Generalized Finite Difference Schemes for the Stochastic HJB Equation [PDF]

SIAM Journal on Numerical Analysis, 2003
Summary: We analyze a class of numerical schemes for solving the HJB equation for stochastic control problems, which enters the framework of Markov chain approximations and generalizes the usual finite difference method. The latter is known to be monotonic, and hence valid, only if the scaled covariance matrix is dominant diagonal.
Hasnaa Zidani, J Frédéric Bonnans
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On Computation of Optimal Switching HJB Equation

Proceedings of the 45th IEEE Conference on Decision and Control, 2006
This paper proposes an algorithm to compute the optimal switching cost from the dynamic programming Hamilton-Jacobi-Bellman (HJB) equations. For the optimal switching control problem, the HJB equation is a System of Quasi-Variational Inequalities (SQVIs) coupled by a nonlinear operator. By exploring the fundamental limit on the number of switches could
Huan Zhang, Matthew R. James
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A new iterative method for discrete HJB equations

Numerische Mathematik, 2008
The goal of this paper is to propose a successive relaxation iterative algorithm for discrete Hamilton-Jacobi-Bellman equation: \((1) \max_{1\leq j\leq K} \{A^JU-F^J\}=0\) where \(A^j \in \mathbb R^{n \times n}, F^j \in \mathbb R^n, j=1,2,\dots K\). Equation (1) is a system of nonsmooth nonlinear equations. A successive iterative scheme, similar to the
Shuzi Zhou, Zhanyong Zou
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Modifications of the PCPT method for HJB equations

AIP Conference Proceedings, 2016
In this paper we will revisit the modification of the piecewise constant policy timestepping (PCPT) method for solving Hamilton-Jacobi-Bellman (HJB) equations. This modification is called piecewise predicted policy timestepping (PPPT) method and if properly used, it may be significantly faster.
I. Kossaczký, M. Ehrhardt, M. Günther
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Dynamic Programming and HJB Equations

1999
In this chapter we turn to study another powerful approach to solving optimal control problems, namely, the method of dynamic programming. Dynamic programming, originated by R. Bellman in the early 1950s, is a mathematical technique for making a sequence of interrelated decisions, which can be applied to many optimization problems (including optimal ...
Jiongmin Yong, Xun Yu Zhou
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Regularity Properties for General HJB Equations: A Backward Stochastic Differential Equation Method

SIAM Journal on Control and Optimization, 2012
In this work we investigate regularity properties of a large class of Hamilton-Jacobi- Bellman (HJB) equations with or without obstacles, which can be stochastically interpreted in the form of a stochastic control system in which nonlinear cost functional is defined with the help of a backward stochastic differential equation (BSDE) or a reflected BSDE.
Rainer Buckdahn, Jianhui Huang
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POD-based feedback control of the burgers equation by solving the evolutionary HJB equation

Computers and Mathematics With Applications, 2005
A numerical method is proposed for solving finite-time horizon suboptimal feedback control problems of distributed parameter systems. The method is based on model reduction by proper orthogonal decomposition (POD), and a local Lax-Friedrichs scheme is used to solve the resulting evolutionary Hamilton-Jacobi-Bellman (HJB) equation. The latter scheme for
K Kunisch
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Viscosity Solutions for HJB Equations

2014
The theory of viscosity solutions was originated by M.G. Crandall and P.L. Lions in the early 80s for the Hamilton–Jacobi equations and later P.L. Lions developed it for the HJB equations (Lions, J Commun PDE 8:1101–1134, 1983; Acta Math 16:243–278, 1988; Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in ...
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Viscosity Solutions to HJB Equations with Hölder Continuous Coefficients

Journal of Optimization Theory and Applications
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jianrui Li, Jinghai Shao, Hui Zhao
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Pathwise Stochastic Control Problems and Stochastic HJB Equations

SIAM Journal on Control and Optimization, 2007
In this paper we study a class of pathwise stochastic control problems in which the optimality is allowed to depend on the paths of exogenous noise (or information). Such a phenomenon can be illustrated by considering a particular investor who wants to take advantage of certain extra information but in a completely legal manner.
Rainer Buckdahn, Jin Ma
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