In this talk, we discuss our work on hybrid glass box/black box optimization, also known as gray box optimization. This problem structure, which bridges classical nonlinear optimization with derivative free optimization, occurs when a subset of model equations is only available via black box evaluations. κ-fully linear approximation models are used to replace the black box function, and a trust region filter algorithm is drives convergence to an optimal solution of the original glass box / black box model. The algorithm is demonstrated on modified optimization benchmarks as well as illustrative examples for chemical process optimization. Then, we discuss our work on extending the use of κ -fully linear models to “short-cut” approximation models. With phase equilibrium as an example, we show how the underlying assumptions of the short-cut model can be “tuned” to build κ -fully linear models that incorporate knowledge about the underlying physics.