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.

Syllabi

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

Course material:

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).