Approximation of an optimal value of a Bolza functional

作者：Pustelnik Jan^*

来源：Optimization, 2013, 62(1): 143-153.

DOI：10.1080/02331934.2011.574697

• Bolza problem
• Hamilton-Jacobi equation
• Hamilton-Jacobi inequality
• optimal control
• numerical approximation
• 49L20
• 34H05
• 93C15
• 65K10

In this article, we show that under reasonable assumptions every Lipschitz-continuous solution to a HamiltonJacobi inequality approximates with a priori known error the optimal value of a respective Bolza functional and that such approximation is stable. The solutions of HamiltonJacobi variational inequalities can be easily obtained by well-known numerical methods as approximate solutions of HamiltonJacobi equations resulting from related Bolza functionals. The main strength of this approach lies in the fact that both precise solution to the HamiltonJacobi PDE and the distance between that solution and its numerical approximation need not be known in order to solve the original Bolza problem.

• 出版日期2013-1-1