Second Order Hamilton-Jacobi Equations in Hilbert Spaces and Stochastic Optimal Control

2002 ◽  
pp. 255-286 ◽  
Author(s):  
Fausto Gozzi
Keyword(s):  
Optimal Control ◽  
Hilbert Spaces ◽  
Stochastic Optimal Control ◽  
Second Order ◽  
Jacobi Equations

scholarly journals On the implicit complementarity problem in Hilbert spaces

1985 ◽  
Vol 32 (2) ◽  
pp. 251-260 ◽  
Author(s):  
G. Isac
Keyword(s):  
Optimal Control ◽  
Variational Inequalities ◽  
Existence Theorem ◽  
Hilbert Spaces ◽  
Stochastic Optimal Control ◽  
Complementarity Problem ◽  
Principal Result ◽  
Implicit Complementarity Problem

We consider in this paper the implicit complementarity problem imposed by quasi-variational inequalities and stochastic optimal control. The principal result is an existence theorem for the implicit complementarity problem in Hilbert spaces.

scholarly journals The subdifferential of the sum of two functions in Banach spaces II. Second order case

1995 ◽  
Vol 51 (2) ◽  
pp. 235-248 ◽  
Author(s):  
Robert Deville ◽  
El Mahjoub El Haddad
Keyword(s):  
Hilbert Spaces ◽  
Type Theorem ◽  
Continuous Functions ◽  
Second Order ◽  
Infinite Dimensional ◽  
Jacobi Operators ◽  
Uniqueness Results ◽  
Lower Semi ◽  
Order Case ◽  
Jacobi Equations

We prove a formula for the second order subdifferential of the sum of two lower semi continuous functions in finite dimensions. This formula yields an Alexandrov type theorem for continuous functions. We derive from this uniqueness results of viscosity solutions of second order Hamilton-Jacobi equations and singlevaluedness of the associated Hamilton-Jacobi operators. We also provide conterexamples in infinite dimensional Hilbert spaces.

scholarly journals High Order Numerical Schemes for Second-Order FBSDEs with Applications to Stochastic Optimal Control

2017 ◽  
Vol 21 (3) ◽  
pp. 808-834 ◽  
Author(s):  
Weidong Zhao ◽  
Tao Zhou ◽  
Tao Kong
Keyword(s):  
Optimal Control ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Euler Method ◽  
Second Order ◽  
High Order ◽  
High Order Accuracy ◽  
Numerical Schemes ◽  
Order Accuracy ◽  
Quantities Of Interest

AbstractThis is one of our series papers on multistep schemes for solving forward backward stochastic differential equations (FBSDEs) and related problems. Here we extend (with non-trivial updates) our multistep schemes in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36 (2014), pp. A1731-A1751] to solve the second-order FBSDEs (2FBSDEs). The key feature of the multistep schemes is that the Euler method is used to discretize the forward SDE, which dramatically reduces the entire computational complexity. Moreover, it is shown that the usual quantities of interest (e.g., the solution tuple (Yt,Zt,At,Γt) of the 2FBSDEs) are still of high order accuracy. Several numerical examples are given to show the effectiveness of the proposed numerical schemes. Applications of our numerical schemes to stochastic optimal control problems are also presented.

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