The use of trust region algorithms to exploit discrepancies in function computation time within optimization models

Computational models in engineering often use a range of analysis functions within the same optimization problem, from finite element models to analyt ical expressions. The computational expense of these models often differs b y orders of magnitude, and practical optimization algorithms should address this discrepancy. In this article, in an effort to reduce the number of ex pensive analyses, a technique is discussed for modifying trust region algor ithms to utilize the inexpensive functions directly when calculating iterat es. The technique is implemented with a trust region algorithm of Yuan and applied to valve event optimization of an internal combustion engine.