Computational Mathematics for Learning and Data Analysis - AA 2024/25

First-order local optimality conditions. A (part of a) proof of a theorem, for the once, because theorems breed algorithms: the steepest descent direction. Second-order local optimality conditions, necessary and sufficient version. A glimpse of the proof for another important concept: directions of negative curvature. Towards global optimization: multivariate convex functions, convexity and continuity, first- and second-order order conditions for convexity. Wrap-up on optimality conditions: (local) optimization is solving systems of nonlinear equations.