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