This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be dir...This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be directly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the ll penalty function and a novel smoothing technique are in-troduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algo-rithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reaCtor operation problem are in agreement with the literature reoorts, and the comoutational efficiency is also high.展开更多
In this paper,we consider optimal control of stochastic differential equations subject to an expected path constraint.The stochastic maximum principle is given for a general optimal stochastic control in terms of cons...In this paper,we consider optimal control of stochastic differential equations subject to an expected path constraint.The stochastic maximum principle is given for a general optimal stochastic control in terms of constrained FBSDEs.In particular,the compensated process in our adjoint equation is deterministic,which seems to be new in the literature.For the typical case of linear stochastic systems and quadratic cost functionals(i.e.,the so-called LQ optimal stochastic control),a verification theorem is established,and the existence and uniqueness of the constrained reflected FBSDEs are also given.展开更多
基金Supported by the National Natural Science Foundation of China(U1162130)the National High Technology Research and Development Program of China(2006AA05Z226)Outstanding Youth Science Foundation of Zhejiang Province(R4100133)
文摘This paper considers dealing with path constraints in the framework of the improved control vector iteration （CVI） approach. Two available ways for enforcing equality path constraints are presented, which can be directly incorporated into the improved CVI approach. Inequality path constraints are much more difficult to deal with, even for small scale problems, because the time intervals where the inequality path constraints are active are unknown in advance. To overcome the challenge, the ll penalty function and a novel smoothing technique are in-troduced, leading to a new effective approach. Moreover, on the basis of the relevant theorems, a numerical algo-rithm is proposed for nonlinear dynamic optimization problems with inequality path constraints. Results obtained from the classic batch reaCtor operation problem are in agreement with the literature reoorts, and the comoutational efficiency is also high.
基金Ying Hu is partially supported by Lebesgue Center of Mathematics“Investissements d’avenir”Program(Grant No.ANR-11-LABX-0020-01)ANR CAESARS(Grant No.ANR-15-CE05-0024)+6 种基金ANR MFG(Grant No.ANR-16-CE40-0015-01)Shanjian Tang is partially supported by the National Science Foundation of China(Grant Nos.11631004 and 12031009)Zuo Quan Xu is partially supported by NSFC(Grant No.11971409)Research Grants Council of Hong Kong(GRF,Grant No.15202421)PolyU-SDU Joint Research Center on Financial MathematicsCAS AMSS-POLYU Joint Laboratory of Applied MathematicsHong Kong Polytechnic University.
文摘In this paper,we consider optimal control of stochastic differential equations subject to an expected path constraint.The stochastic maximum principle is given for a general optimal stochastic control in terms of constrained FBSDEs.In particular,the compensated process in our adjoint equation is deterministic,which seems to be new in the literature.For the typical case of linear stochastic systems and quadratic cost functionals(i.e.,the so-called LQ optimal stochastic control),a verification theorem is established,and the existence and uniqueness of the constrained reflected FBSDEs are also given.
