Use of optimization in applications with errors

We consider the basic problem of using optimization in situations where the quantities involved cannot be evaluated precisely. An example we have considered in the past (see reference [1]) is the circuit design optimization problem. The objective in such a problem is to determine values for certain parameters in the circuits that optimize some measure of circuit performance. This measure or criterion is evaluated by solving a system of nonlinear algebraic and differential equations. These equations can be solved to a specified degree of accuracy, but the cost of a function/ gradient evaluation can increase significantly when the accuracy is increased. In this situation the function and gradient evaluations contain approximately the same percentage errors. Initial tests as represented in [1] indicated that variable metric schemes can be reliable when applied to such problems. Many other applications exist. In this talk we examine this question of computing an 'optimal' solution in the presence of such errors.