A unified treatment of maximum principle and dynamic programming in stochastic controls
- 1 September 1991
- journal article
- research article
- Published by Taylor & Francis in Stochastics and Stochastic Reports
- Vol. 36 (3-4) , 137-161
- https://doi.org/10.1080/17442509108833715
Abstract
An optimal stochastic control problem is considered in this paper, where the diffusion coefficient also depends on the control and is possibly degenerate. In addition to the usual adjoint process, a second-order adjoint process is introduced. Some relationships between the value function and the adjoint processes are presented via the “super- and sub-differential” which is related to the viscosity solution, without assuming the smoothness of the value function. The maximum principle, dynamic programming and their connections are then established within a unified framework of viscosity solutionKeywords
This publication has 13 references indexed in Scilit:
- The Relationship between the Maximum Principle and Dynamic ProgrammingSIAM Journal on Control and Optimization, 1987
- The Pontryagin maximum principle from dynamic programming and viscosity solutions to first-order partial differential equationsTransactions of the American Mathematical Society, 1986
- Local Optimality Conditions and Lipschitzian Solutions to the Hamilton–Jacobi EquationSIAM Journal on Control and Optimization, 1983
- Viscosity solutions of Hamilton-Jacobi equationsTransactions of the American Mathematical Society, 1983
- Optimal control of diffusion processes and hamilton–jacobi–bellman equations part 2 : viscosity solutions and uniquenessCommunications in Partial Differential Equations, 1983
- Auxiliary PropositionsPublished by Springer Nature ,1980
- An Introductory Approach to Duality in Optimal Stochastic ControlSIAM Review, 1978
- The Maximum Principle under Minimal HypothesesSIAM Journal on Control and Optimization, 1976
- Deterministic and Stochastic Optimal ControlPublished by Springer Nature ,1975
- Necessary Conditions for Continuous Parameter Stochastic Optimization ProblemsSIAM Journal on Control, 1972