Lecture notes Basic tools: inf/sup, compactness in R^n, implicit function theorem etc., by Harald Krogstad Compactness, lower semi-continuity, and existence of solutions Convergence of descent methods with backtracking (Armijo) linesearch Optimality conditions for constrained problems over convex sets Representation theorem for polyhedral sets Sufficiency of KKT conditions for convex programs Intro to calculus of variations