# Numerical procedure to approximate a singular optimal control problem

Silvia C. Di Marco; Roberto L.V. González

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

- Volume: 41, Issue: 3, page 461-484
- ISSN: 0764-583X

## Access Full Article

top## Abstract

top## How to cite

topDi Marco, Silvia C., and González, Roberto L.V.. "Numerical procedure to approximate a singular optimal control problem." ESAIM: Mathematical Modelling and Numerical Analysis 41.3 (2007): 461-484. <http://eudml.org/doc/250069>.

@article{DiMarco2007,

abstract = { In this work we deal with the numerical solution of a
Hamilton-Jacobi-Bellman (HJB) equation with infinitely many
solutions. To compute the maximal solution – the optimal
cost of the original optimal control problem – we present a
complete discrete method based on the use of some finite elements
and penalization techniques.
},

author = {Di Marco, Silvia C., González, Roberto L.V.},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Multiple solutions; eikonal equation;
singular optimal control problems; penalization methods; numerical
approximation.; Hamilton-Jacobi-Bellman equation; maximal solution},

language = {eng},

month = {8},

number = {3},

pages = {461-484},

publisher = {EDP Sciences},

title = {Numerical procedure to approximate a singular optimal control problem},

url = {http://eudml.org/doc/250069},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Di Marco, Silvia C.

AU - González, Roberto L.V.

TI - Numerical procedure to approximate a singular optimal control problem

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2007/8//

PB - EDP Sciences

VL - 41

IS - 3

SP - 461

EP - 484

AB - In this work we deal with the numerical solution of a
Hamilton-Jacobi-Bellman (HJB) equation with infinitely many
solutions. To compute the maximal solution – the optimal
cost of the original optimal control problem – we present a
complete discrete method based on the use of some finite elements
and penalization techniques.

LA - eng

KW - Multiple solutions; eikonal equation;
singular optimal control problems; penalization methods; numerical
approximation.; Hamilton-Jacobi-Bellman equation; maximal solution

UR - http://eudml.org/doc/250069

ER -

## References

top- G. Barles and P.E. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations. Asymptotic Anal.4 (1991) 271–283. Zbl0729.65077
- M.J. Brooks and K.P. Horn, Shape from shading. MIT Press, Cambridge, MA (1989). Zbl0629.65125
- F. Camilli and L. Grüne, Numerical approximation of the maximal solutions for a class of degenerate Hamilton-Jacobi equations. SIAM J. Num. Anal.38 (2000) 1540–1560. Zbl0988.65077
- F. Camilli and A. Siconolfi, Maximal subsolutions for a class of degenerate Hamilton-Jacobi problems. Indiana Univ. Math. J.48 (1999) 271–283. Zbl0939.49019
- E. Cristiani and M. Falcone, Fast semi-Lagrangian schemes for the eikonal equation and applications. http://cpde.iac.rm.cnr.it/file_ uploaded/EFX30053.pdf. Zbl1154.65053
- S.C. Di Marco and R.L.V. González, Minimax optimal control problems. Numerical analysis of the finite horizon case. ESAIM: M2AN33 (1999) 23–54.
- S.C. Di Marco and R.L.V. González, Numerical approximation of a singular optimal control problem. Anales de Simposio Argentino en Investigación Operativa, 32° Jornadas Argentinas de Informática e Investigación Operativa, Sociedad Argentina de Informática e Investigación Operativa (2003).
- S.C. Di Marco and R.L.V. González, Penalization methods in the numerical solution of the eikonal equation. Mecánica Computacional, Vol XXII, ISSN 1666–6070 (2003).
- H. Ishii and M. Ramaswamy, Uniqueness results for a class of Hamilton-Jacobi equations with singular coefficients. Comm. Partial Diff. Eq.20 (1995) 2187–2213. Zbl0842.35019
- P.-L. Lions, E. Rouy and A. Tourin, Shape from shading, viscosity solutions and edges. Numer. Math.64 (1993) 323–353. Zbl0804.68160
- J. Sethian, Fast marching methods. SIAM Rev.41 (1999) 199–235. Zbl0926.65106
- H. Whitney, A function not constant on a connected set of critical points. Duke Math. J.1 (1935) 514–517. Zbl0013.05801

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.