Convex Optimization and Analysis - 463/663 - Fall 2002

Background: Euclidean spaces and symmetric matrices.
Inequality Constraints: Optimality Conditions; Theorems of the Alternative; Max-functions.
Fenchel Duality: Subgradients and Convex Functions; The Value Function; The Fenchel Conjugate.
Convex Analysis: Continuity of Convex Functions; Fenchel Biconjugation; Lagrangian Duality.
Nonsmooth Optimization: Generalized Derivatives; Regularity adn Strict Differentiability; Tangent Cones.
Karush-Kuhn-Tucker Theory: Introduction to Metric Regularity; The KKT Theorem.

HOMEWORK LIST- C &O 463/663

Homework #1 (Background)
Due: Friday, Sept. 13, 2001 (at start of class)
Reading

Chapter 1 (pages 1-14)
For your interest only: NEOS Guide Optimization Tree
Problems

Pages 5-8: #1,4,5,10,11
Homework #2 (Symmetric Matrices)
Due: Wednsday Sept. 18, 2002 (at start of class)
Reading
- Section 2.1 in the text (pages 15-18)
- For your interest only: Decision Tree for Optimization Software
Problems
- Page 11, Problems 5,6 and Page 12 Problem 11.
Homework #3 (Optimality Conditions)
Due: Friday Sept. 27, 2002 (at start of class)
Reading
- Section 2.2 in the text (pages 23-25)
Problems
- Page 19-20, Problems 4,5,8.
Homework #4 (Optimality Conditions cont...)
Due: Monday Oct. 7, 2002 (at start of class)
Reading
- Sections 2.3 and 3.1 in the text.
Problems
- Pages 25-26, Problems 4,5,8 and Pages 30-31 2,4.
Homework #5 (Fenchel Duality)
Due: Wednsday Oct. 16, 2002 (at start of class)
Reading
- Sections 3.2 and 3.3 in the text.
Problems
- Pages 37-42, Problems 4,9,12,20,21.
Homework #6 (Fenchel Duality)
Due: Friday Nov. 1, 2002 (at start of class)
Problems
- Pages 45-48, Problems 4,8,9
- Find the Lagrangian dual of the SDP:
  max trace(QX) s.t. diag(X)=e, X psd
  where Q=Q^T is a given real symmetric matrix and e is the vector of all ones.
Homework #7 (Fenchel Duality)
Due: Wed. Nov. 13, 2002 (at start of class)
Problems
- Pages 55, Problems 2,13,20,24

, by Henry Wolkowicz