This paper derives necessary and sufficient conditions of optimality in the form of a stochastic maximum principle for relaxed and strict optimal control problems with jumps.These problems are governed by multi-dimens...This paper derives necessary and sufficient conditions of optimality in the form of a stochastic maximum principle for relaxed and strict optimal control problems with jumps.These problems are governed by multi-dimensional forward-backward doubly stochastic differential equations(FBDSDEs)with Poisson jumps and has firstly relaxed controls,which are measure-valued processes,and secondly,as an application,the authors allow them to have strict controls.The FBDSDEs with jumps are fully-coupled,the forward and backward equations work in different Euclidean spaces in general,the backward equation is Markovian,and the control problems are considered under full information or partial information in terms ofσ-algebras that provide such information.The formulation of these equations as well as performance functionals are given in abstract forms to allow the possibility to cover most of the applications available in the literature.Moreover,coefficients of such equations are allowed to depend on control variables.展开更多
In this paper, a Newton-conjugate gradient （CG） augmented Lagrangian method is proposed for solving the path constrained dynamic process optimization problems. The path constraints are simplified as a single final t...In this paper, a Newton-conjugate gradient （CG） augmented Lagrangian method is proposed for solving the path constrained dynamic process optimization problems. The path constraints are simplified as a single final time constraint by using a novel constraint aggregation function. Then, a control vector parameterization （CVP） approach is applied to convert the constraints simplified dynamic optimization problem into a nonlinear programming （NLP） problem with inequality constraints. By constructing an augmented Lagrangian function, the inequality constraints are introduced into the augmented objective function, and a box constrained NLP problem is generated. Then, a linear search Newton-CG approach, also known as truncated Newton （TN） approach, is applied to solve the problem. By constructing the Hamiltonian functions of objective and constraint functions, two adjoint systems are generated to calculate the gradients which are needed in the process of NLP solution. Simulation examlales demonstrate the effectiveness of the algorithm.展开更多
基金Qassim University,represented by the Deanship of Scientific Research under Grant No.SR-D-015-3352the Algerian PRFU under Grant No.C00L03UN07120180005。
文摘This paper derives necessary and sufficient conditions of optimality in the form of a stochastic maximum principle for relaxed and strict optimal control problems with jumps.These problems are governed by multi-dimensional forward-backward doubly stochastic differential equations(FBDSDEs)with Poisson jumps and has firstly relaxed controls,which are measure-valued processes,and secondly,as an application,the authors allow them to have strict controls.The FBDSDEs with jumps are fully-coupled,the forward and backward equations work in different Euclidean spaces in general,the backward equation is Markovian,and the control problems are considered under full information or partial information in terms ofσ-algebras that provide such information.The formulation of these equations as well as performance functionals are given in abstract forms to allow the possibility to cover most of the applications available in the literature.Moreover,coefficients of such equations are allowed to depend on control variables.
基金supported by the Natural Science Foundation of China (No. 60974039)the National Science and Technology Major Project (No.2008ZX05011)
文摘In this paper, a Newton-conjugate gradient （CG） augmented Lagrangian method is proposed for solving the path constrained dynamic process optimization problems. The path constraints are simplified as a single final time constraint by using a novel constraint aggregation function. Then, a control vector parameterization （CVP） approach is applied to convert the constraints simplified dynamic optimization problem into a nonlinear programming （NLP） problem with inequality constraints. By constructing an augmented Lagrangian function, the inequality constraints are introduced into the augmented objective function, and a box constrained NLP problem is generated. Then, a linear search Newton-CG approach, also known as truncated Newton （TN） approach, is applied to solve the problem. By constructing the Hamiltonian functions of objective and constraint functions, two adjoint systems are generated to calculate the gradients which are needed in the process of NLP solution. Simulation examlales demonstrate the effectiveness of the algorithm.
