Optimal design models contain parameters that are considered fixed during the optimization process. When these parameters change values, the mathematical properties of the model and the physical behavior of the underlying engineering system may change drastically. This article examines how large changes in one parameter affect the optimal solution and the type of singularities that may be encountered. The theory presented extends parametric optimization beyond the usual sensitivity analysis, and can be used as a modeling tool or as a rigorous treatment of related problems, such as multi-level decomposition. The algorithmic implementation and numerical examples are presented in a sequel article.

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