ABSTRACT
This chapter defines the L∞-norm estimation problem, provides the conditions under which a solution will be optimal, and discusses algorithms which can be used to solve this problem. The nondifferentiable Loo-norm estimation problem more frequently referred to as Chebychev estimation is of importance when one's objective is to minimize the maximum absolute error. It is also a special case of the minimax problem which is encountered in Game Theory. Since L∞-norm estimation is a special case of the minimax problem it will be appropriate to consider it separately. W. Murray and M. Overton developed a procedure for solving the nonlinear minimax problem. Overton adapted this approach to solve the nonlinear L∞-norm estimation problem. S. P. Han developed a method for solving the minimax problem. The method possesses the attractive features of the usual quasi-Newton methods of differentiable unconstrained optimization. It can therefore be considered as an extension of quasi-Newton methods to solve nondifferentiable problems.
