Lecture 8.2: theory of gradients and Hessians towards optimality conditions
Completion requirements
Derivatives in R^n: partial derivatives, directional derivatives, gradient. Why do we care: directions of descent. Differentiability and the multivariate first-order model. The many ways in which a function can be non differentiable. Gradient: geometric interpretation with sublevel sets. Jakobian, second-order derivatives, Hessian matrix and the second-order model. The nice and very nice classes of functions: C^1 and C^2.