The Lagrange and the vanishing discount techniques to controlled diffusions with cost constraints
| Autor: | Armando F. Mendoza-Pérez, Beatris Adriana Escobedo-Trujillo, Héctor Jasso-Fuentes |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Mathematical optimization
021103 operations research Applied Mathematics Stochastic game 0211 other engineering and technologies 02 engineering and technology Function (mathematics) Optimal control 01 natural sciences Constraint (information theory) Dynamic programming 010104 statistics & probability symbols.namesake Constraint algorithm Lagrange multiplier symbols 0101 mathematics Constant (mathematics) Analysis Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 437:999-1035 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2016.01.036 |
| Popis: | In this paper we introduce two useful methods to compute optimal control policies for either the discounted or the average payoff criterion with cost constraints when the dynamic system evolves as a n -dimensional diffusion processes. As for the attribute “cost constraints” we mean the coexistence of a given cost function that in general is dominated above by another function (in particular by a constant) playing the role of an extra constraint in the control model. To deduce optimality results for the discounted case, we employ the Lagrange multipliers technique along with dynamic programming arguments. Then, the vanishing discount method is applied to easily obtain average optimal policies. We support our theory by providing an example on pollution accumulation problem. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect