# An algorithm for construction of ε-value functions for the Bolza control problem

International Journal of Applied Mathematics and Computer Science (2001)

- Volume: 11, Issue: 2, page 391-428
- ISSN: 1641-876X

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topJacewicz, Edyta. "An algorithm for construction of ε-value functions for the Bolza control problem." International Journal of Applied Mathematics and Computer Science 11.2 (2001): 391-428. <http://eudml.org/doc/207513>.

@article{Jacewicz2001,

abstract = {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 ε-value function is defined as an approximation for the value function being a solution to the Hamilton-Jacobi equation. The paper shows how an ε-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.},

author = {Jacewicz, Edyta},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {ε-value function; Hamilton-Jacobi equation; non-linear optimisation; approximate minimum; dynamic programming; Bolza problem; optimal control; nonlinear optimization; -value function; approximation minimum},

language = {eng},

number = {2},

pages = {391-428},

title = {An algorithm for construction of ε-value functions for the Bolza control problem},

url = {http://eudml.org/doc/207513},

volume = {11},

year = {2001},

}

TY - JOUR

AU - Jacewicz, Edyta

TI - An algorithm for construction of ε-value functions for the Bolza control problem

JO - International Journal of Applied Mathematics and Computer Science

PY - 2001

VL - 11

IS - 2

SP - 391

EP - 428

AB - 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 ε-value function is defined as an approximation for the value function being a solution to the Hamilton-Jacobi equation. The paper shows how an ε-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.

LA - eng

KW - ε-value function; Hamilton-Jacobi equation; non-linear optimisation; approximate minimum; dynamic programming; Bolza problem; optimal control; nonlinear optimization; -value function; approximation minimum

UR - http://eudml.org/doc/207513

ER -

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