EE617: Linear and Convex Optimization (Fall 2017)

Instructor: Yuanzhang Xiao, xyz.xiao@gmail.com

Lectures: Monday and Wednesday 3:00pm - 4:15pm, Holmes Hall 242

Office Hours: Tuesday and Thursday 3:00pm - 4:15pm (or by appointment), POST Building 201G

Text Book: Convex Optimization by Stephen Boyd and Lieven Vandenberghe

Software: CVX in Matlab or CVXPY in Python

Grading Policy:

  • 5 homework assignments (50%)

  • mid-term exam (20%, open book)

  • final project (30%)

Schedule, Lecture Notes, and Reading

The schedule is subject to adjustment.

Theory (Aug. 21 - Sep. 20, 5 weeks)

  1. Introduction and Motivation (Lecture Notes, Read: Chapter 1)

  2. Convex Sets (Lecture Notes, Read: Chapter 2.1-2.3, 2.5)

  3. Convex Functions (Lecture Notes, Read: Chapter 3.1, 3.2, 3.4)

  4. Convex Optimization Problems (Lecture Notes, Read: Chapter 4.1-4.5)

  5. Optimality Condition and Duality (Lecture Notes, Read: Chapter 5.1-5.8)

Applications (Sep. 25 - Oct. 18, 4 weeks)

  1. Applications in Machine Learning (Lecture Notes)

  2. Applications in Signal Processing (Lecture Notes)

  3. Applications in Wireless Communications (Lecture Notes)

  4. Applications in Smart Grids (Lecture Notes)

Review Session For Mid-Term Exam (Oct. 23)

Mid-Term Exam (Oct. 25) (Exam and Solution)

Algorithm (Oct. 30 - Nov. 22, 4 weeks)

  1. CVX in Matlab and CVXPY in Python (Lecture Notes)

  2. Unconstrained Minimization (Lecture Notes)

  3. Equality Constrained Minimization (Lecture Notes)

  4. Interior-Point Methods (Lecture Notes)

Advanced Topics (Nov. 27 - Dec. 6, 2 weeks)

  1. Convex Relaxation For Nonconvex Problems (Lecture Notes)

  2. Gradient Descent in Machine Learning (Lecture Notes)

  3. Softmax Regression and Neural Networks (Lecture Notes)

Final Project (Dec. 15)

Homework

Homework 1 (due Oct. 23) (Solution)

  • exercises 2.7, 2.11, 2.12 (a,b,c,d,e,g), 2.19, 2.24

  • exercises 3.2, 3.19, 3.20, 3.21, 3.23

Homework 2 (due Oct. 23) (Solution)

  • exercises 4.7, 4.11, 4.15, 4.23, 4.33

  • exercises 5.5, 5.11, 5.21 (a,b,c), 5.26, 5.27

Homework 3 (due Nov. 15) (Solution in Matlab, Solution in Python)

Homework 4 (due Dec. 4)

Homework 5 (due Dec. 4)