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Unconstrained Optimality Conditions

This video is part of the set of lectures for SE 413, an engineering design optimization (EDO) course at UIUC. This video introduces the mathematical optimality conditions for unconstrained optimization problems involving continuous smooth objective functions. Motivation for learning unconstrained optimization theory and algorithms in the context of EDO is provided, followed by a derivation of optimality conditions for both univariate and multivariate cases. Both graphical and mathematical approaches are utilized to introduce optimality conditions. A strategy for analytical solution of optimization problems based on optimality conditions is introduced, and then demonstrated using a multivariate example. A broad view of the relationship between optimality conditions and selected solution algorithms is presented, demonstrating how multiple complementary derivation paths result in useful insights. The core goal of learning this material is to help students gain the knowledge and creativity required to be more effective in making problem formulation decisions, implementing numerical optimization algorithms, and performing solution analysis as part of the EDO problem formulation cycle. The following published Google doc lists the sequence of SE 413 lecture videos and provides links to those that are publicly available: https://tinyurl.com/fg37hj77