@article{M2AN_1999__33_1_23_0, author = {Di Marco, Silvia C. and Gonz\'alez, Roberto L. V.}, title = {Minimax optimal control problems. {Numerical} analysis of the finite horizon case}, journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {23--54}, publisher = {EDP-Sciences}, volume = {33}, number = {1}, year = {1999}, mrnumber = {1685742}, zbl = {0918.65049}, language = {en}, url = {http://www.numdam.org/item/M2AN_1999__33_1_23_0/} }
TY - JOUR AU - Di Marco, Silvia C. AU - González, Roberto L. V. TI - Minimax optimal control problems. Numerical analysis of the finite horizon case JO - ESAIM: Modélisation mathématique et analyse numérique PY - 1999 SP - 23 EP - 54 VL - 33 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/item/M2AN_1999__33_1_23_0/ LA - en ID - M2AN_1999__33_1_23_0 ER -
%0 Journal Article %A Di Marco, Silvia C. %A González, Roberto L. V. %T Minimax optimal control problems. Numerical analysis of the finite horizon case %J ESAIM: Modélisation mathématique et analyse numérique %D 1999 %P 23-54 %V 33 %N 1 %I EDP-Sciences %U http://www.numdam.org/item/M2AN_1999__33_1_23_0/ %G en %F M2AN_1999__33_1_23_0
Di Marco, Silvia C.; González, Roberto L. V. Minimax optimal control problems. Numerical analysis of the finite horizon case. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 1, pp. 23-54. http://www.numdam.org/item/M2AN_1999__33_1_23_0/
[1] Differential inclusions. Springer-Verlag, New York (1984). | MR | Zbl
and ,[2] Optimal control on the L∞ norm of a diffusion process. SIAM J. Contr. Opt. 32 (1994) 612-634. | MR | Zbl
, and ,[3] Convergence of numerical schemes for parabolic equations arising in finace theory. Math. Models Met. Appl. Sci. 5 (1995) 125-143. | MR | Zbl
, and ,[4] Differential games with maximum cost. Nonlinear Analysis, Theory, Methods and Applications 14 (1990) 971-989. | MR | Zbl
,[5] The Pontryagin maximum principle for minimax problems of optimal control. Nonlinear Analysis, Theory, Methods and Applications 15 (1990) 1155-1165. | MR | Zbl
,[6] Averaging in Lagrange and minimax problems of optimal control. SIAM J. Contr. Opt. 31 (1930) 1630-1652. | MR | Zbl
,[7] Optimal control and calculus of variations in L∞, in Optimal Control in Differential Equations. N.H. Pavel and Marcel Dekker Eds., New York (1994). | MR | Zbl
,[8] The Bellman equation for minimizing the maximum cost. Nonlinear Analysis, Theory, Methods and Applications 13 (1989) 1067-1090. | MR | Zbl
and ,[9] Relaxed minimax control. SIAM J. Contr. Opt. 33 (1995) 1028-1039. | MR | Zbl
and ,[10] Optimal control and differential games with measures. Nonlinear Analysis, Theory, Methods and Applications 21 (1993) 241-268. | MR | Zbl
, and ,[11] On a discrete approximation of the Hamilton-Jacobi equation of dynamic programming. Appl. Math. Optim. 10 (1983) 367-377. | MR | Zbl
,[12] Discrete dynamic programming and viscosity solutions of the Bellman equation. Ann. Inst. Henry Poincaré. Anal. Non-lin. 6 (1989) 161-184. | Numdam | MR | Zbl
and ,[13] Approximate solution of the Bellman equation of determmistic control theory. Appl. Math. Optim. 11 (1984) 161-181. | MR
and ,[14] Discrete maximum principle for finite-difference operators. Aequations Math. 4 (1970) 338-352. | MR | Zbl
,[15] Direct methods in the calculus of variations Springer-Verlag, Berlin (1987). | Zbl
,[16] Une procedure numérique pour la minimisation du coût maximum. C. R. Acad. Sci. Pans, Série I 321 (1995) 869-874. | MR | Zbl
and ,[17] A minimax optimal control problem wih infinite horizon. Rapport de Recherche N°2945, INRIA, Rocquencourt (1996).
and ,[18] Differential games. Wiley-Interscience, New York (1971). | MR | Zbl
,[19] On deterministic control problems: An approximation procedure for the optimal cost, Parts 1 and 2, SIAM J. Contr. Opt. 23 (1985) 242-285. | MR | Zbl
and ,[20] On a discrete time approximation of the Hamilton-Jacobi equation of dynamic programming, Rapport de Recherche N°1375, INRIA, Rocquencourt (1990).
and ,[21] On the rate of convergence of fully discrete solutions of Hamilton-Jacobi equations, Rapport de Recherche N°1376, INRIA, Rocquencourt (1991). | MR
and ,[22] Sur l'ordre de convergence des solutions discrétisées en temps et en espace de l'équation de Hamilton-Jacobi, C. R. Acad. Sci., Paris, Série I 314 (1992) 479-482. | MR | Zbl
and ,[23] An analysis of the finite element method Prentice-Hall, Englewood Cliffs, New Jersey (1973). | MR | Zbl
and ,