Geodesic
An Algorithm for Construction of varepsilon-Value Functions for the Bolza Control Problem
International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) no. 2, pp. 391-428.

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The problem considered is that of approximate numerical minimisation of the non-linear control problem of Bolza. Starting from the classical dynamic programming method of Bellman, an varepsilon-value function is defined as an approximation for the value function being a solution to the Hamilton-Jacobi equation. The paper shows how an varepsilon-value function which maintains suitable properties analogous to the original Hamilton-Jacobi value function can be constructed using a stable numerical algorithm. The paper shows the numerical closeness of the approximate minimum to the infimum of the Bolza functional.
Keywords: nonlinear optimization, Bolza problem, optimal control, Hamilton-Jacobi equation, dynamic programming, varepsilon-value function, approximate minimum
Mots-clés : optymalizacja nieliniowa, sterowanie optymalne 
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     title = {An {Algorithm} for {Construction} of {varepsilon-Value} {Functions} for the {Bolza} {Control} {Problem}},
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Jacewicz, E. An Algorithm for Construction of varepsilon-Value Functions for the Bolza Control Problem. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) no. 2, pp. 391-428. https://geodesic-test.mathdoc.fr/item/IJAMCS_2001_11_2_a5/