High-Order Extended Maximum Principles for Optimal Control Problems with Non-Regular Constraints

1998 ◽  
pp. 298-325
Author(s):  
Urszula Ledzewicz ◽  
Heinz Schättler
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
High Order ◽  
Maximum Principles ◽  
Control Problems

scholarly journals Conjugate duality in stochastic controls with delay

2017 ◽  
Vol 49 (4) ◽  
pp. 1011-1036
Author(s):  
Zimeng Wang ◽  
David J. Hodge ◽  
Huiling Le
Keyword(s):  
Optimal Control ◽  
Stochastic Optimal Control ◽  
Optimal Control Problems ◽  
Maximum Principles ◽  
Conjugate Duality ◽  
Control Problems ◽  
Convex Problem ◽  
Stochastic Controls ◽  
The Relationship ◽  
Equations With Delay

AbstractIn this paper we use the method of conjugate duality to investigate a class of stochastic optimal control problems where state systems are described by stochastic differential equations with delay. For this, we first analyse a stochastic convex problem with delay and derive the expression for the corresponding dual problem. This enables us to obtain the relationship between the optimalities for the two problems. Then, by linking stochastic optimal control problems with delay with a particular type of stochastic convex problem, the result for the latter leads to sufficient maximum principles for the former.

scholarly journals Fully Coupled Mean-Field Forward-Backward Stochastic Differential Equations and Stochastic Maximum Principle

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Hui Min ◽  
Ying Peng ◽  
Yongli Qin
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Backward Stochastic Differential Equations ◽  
Maximum Principles ◽  
Control Problems ◽  
Linear Quadratic Optimal Control ◽  
Fully Coupled

We discuss a new type of fully coupled forward-backward stochastic differential equations (FBSDEs) whose coefficients depend on the states of the solution processes as well as their expected values, and we call them fully coupled mean-field forward-backward stochastic differential equations (mean-field FBSDEs). We first prove the existence and the uniqueness theorem of such mean-field FBSDEs under some certain monotonicity conditions and show the continuity property of the solutions with respect to the parameters. Then we discuss the stochastic optimal control problems of mean-field FBSDEs. The stochastic maximum principles are derived and the related mean-field linear quadratic optimal control problems are also discussed.

scholarly journals Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations

2011 ◽  
Vol 43 (02) ◽  
pp. 572-596 ◽  
Author(s):  
Bernt Øksendal ◽  
Agnès Sulem ◽  
Tusheng Zhang
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Optimal Control Problems ◽  
Backward Stochastic Differential Equation ◽  
Maximum Principles ◽  
Optimal Consumption ◽  
Control Problems ◽  
Stochastic Delay ◽  
Stochastic Delay Equations

We study optimal control problems for (time-)delayed stochastic differential equations with jumps. We establish sufficient and necessary stochastic maximum principles for an optimal control of such systems. The associated adjoint processes are shown to satisfy a (time-)advanced backward stochastic differential equation (ABSDE). Several results on existence and uniqueness of such ABSDEs are shown. The results are illustrated by an application to optimal consumption from a cash flow with delay.

scholarly journals Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations

2011 ◽  
Vol 43 (2) ◽  
pp. 572-596 ◽  
Author(s):  
Bernt Øksendal ◽  
Agnès Sulem ◽  
Tusheng Zhang
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Optimal Control Problems ◽  
Backward Stochastic Differential Equation ◽  
Maximum Principles ◽  
Optimal Consumption ◽  
Control Problems ◽  
Stochastic Delay ◽  
Stochastic Delay Equations

We study optimal control problems for (time-)delayed stochastic differential equations with jumps. We establish sufficient and necessary stochastic maximum principles for an optimal control of such systems. The associated adjoint processes are shown to satisfy a (time-)advanced backward stochastic differential equation (ABSDE). Several results on existence and uniqueness of such ABSDEs are shown. The results are illustrated by an application to optimal consumption from a cash flow with delay.

A Survey of the Maximum Principles for Optimal Control Problems with State Constraints

SIAM Review ◽  
1995 ◽  
Vol 37 (2) ◽  
pp. 181-218 ◽  
Author(s):  
Richard F. Hartl ◽  
Suresh P. Sethi ◽  
Raymond G. Vickson
Keyword(s):  
Optimal Control ◽  
State Constraints ◽  
Optimal Control Problems ◽  
Maximum Principles ◽  
Control Problems
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