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Numerical procedure for minimizing the maximum cost. (Une procédure numérique pour la minimisation du coût maximum.) (French. Abridged English version) Zbl 0837.65066

Summary: We consider the numerical solution of a minimax optimal control problem, where the cost to be minimized is the maximum of a function which depends on the state and the control. We present an approximation method which employs both discretization on time and on spatial variables. In this way, we obtain a computational implementable fully discrete problem. We give an optimal estimate for the error between the approximated solution and the optimal cost of the original problem.

MSC:

65K10 Numerical optimization and variational techniques
49M15 Newton-type methods
49J15 Existence theories for optimal control problems involving ordinary differential equations
49J35 Existence of solutions for minimax problems
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