Sample Problems for Nonsmooth Equations

Abstract

A large part of the management and engineering sciences is concerned with the determination of certain unknown quantities. One often assumes that the unknown quantity is determined by some real-world process which can be modeled in mathematical terms. The model may be used to determine the quantity either by more or less sophisticated mathematical methods or by simulating the underlying real-world process on a computer. However, in many situations one is either not able to specify an accurate mathematical model or the model is too complicated to be algorithmically tractable. Being interested in a quantity rather than in a realistic model of the process which determines the quantity, one can often find a way out of the dilemma by specifying a set of conditions which the demanded quantity necessarily satisfies, in the hope that these conditions are easier to find and simpler to treat than a realistic mathematical model of the situation. In order for the necessary conditions to be of practical value, they have to be formulated in algorithmically tractable mathematical terms, for instance, as a system of equations and inequalities.