On optimization over a small implicitly defined feasible region

Abstract

In some applications there occurs optimization problems with small implicitly defined feasible regions and with objective functions not defined outside of the feasible regions. The problems we wish to consider pose a further challenge. The objective function may be non-differentiable and even discontinuous. The problems of interest are normally obtained by means of computer simulation causing some discontinuities and small noise added to the function values. A set of test functions is proposed generalizing the properties of a known problem of optimal process design in oil industry. Several algorithms aimed to the described problemare proposed and implemented. The algorithms are compared experimentally using the proposed testing functions and the mentioned practical problem. The testing results are presented and discussed.