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Robust Lipschitzian properties of set-valued mappings and marginal functions play a crucial role in many aspects of variational analysis and its applications, especially for issues related to variational stability and [...]

The calculus of stationary points or indirect optimization is noted for rapid speed. It's speed is realized in an analytical representation of the Hessian and a polynomial fit of both the objective function and the constraints. Constraints are treated as active using Lagrangian multipliers. Because the algorithm's speed is so rapid, the problem can be repeated multiple times with random starting guesses to circumvent the possibility of encountering local wells. Both an analytic and an actual field problem are considered by way of providing examples of the technique. Index terms - optimization, functional approximations, gradients

Operations of addition and restriction are demonstrated to be continuous, given the usual constrain qualifications, and these results are applicable for convex programming. The results are valid for normed linear spaces without completedness being necessary. The approximation results can also be applied in a situation where X is a Banach space, giving a generic theorem which can be used for problems of the constrained convex type.