Intended audience: Ph.D. students
Outline: A fast-paced introduction to Convex Analysis, directed by end-goals in Optimization
Prerequisites: Knowledge of Advanced Calculus
Main subjects: Convex sets, separation theorems, convex functions, subgradient calculus, Kuhn-Tucker theorem, duality theory, generalized gradients.
Notes 1: On Subdifferential Calculus. Typo: in line 1 of proof Thm. A.2 "sup" should be "inf".
Notes 2: Lagrangian and perturbational duality I
Notes 3: Perturbational duality (continued) and applications
Notes 4: On generalized gradients and optimization
Slides lecture 13-9-2010
Slides lecture 20-9-2010
Slides lecture 27-9-2010
Slides lectures 4-10-2010
Slides lectures 11-10-2010 and first hour 18-10-2010
Slides lecture 18-10-2010 (second hour)
Slides lecture 25-10-2010 (first hour)
Slides lecture 25-10-2010 (second hour)
Slides final lecture 1-11-2010
Homework assignments: Three sets of problems will be distributed, namely on 27-9, 18-10 and 1-11 (the end of the course). Respective turn-in dates are 18-10 at 10:15 a.m., 3-11 at 6:00 p.m. (ordinary mail with date stamp 3-11 is also acceptable) and 6-12 at 11:00 p.m. (ordinary mail with date stamp 6-12 is also acceptable).