Week

Topics

Text Reference

Assignments

1/07

Introduction; Motivating Example: Data Fitting.

Basic Concepts: Vector Space, Norm, Vector Calculus, Linear Algebra.

Chapter 1

Appendix A

1/14

Gradient and Hessian of functions. Functions of matrices. Convex Sets.

Chapter 2

1/21

Convex functions. First-order and Second-order conditions for differentiable convex functions. Properties of Convex Functions.

Chapter 3

HW #1

Due Jan 23

1/28

Convex optimization problems. Local and global optimal solutions of convex optimization problems.

Chapter 4

2/04

Linear Programming. Quadratic programming. Quadratically constrained quadratic programming. Second-order cone programming. Robust linear programming.

Chapter 4

(live on 2/18)

Least-squares problems. Optimal control problem. Geometric programming. Semi-definite programming. SDP relaxation.

Chapter 4

HW #2

Due Feb 27

Study Break

2/25

Theory: Lagrangian. Dual optimization problem. Duality gap. Slater’s condition. Sensitivity analysis.

Chapter 5,

Rockafellar: Sec. 33

Project Proposal

Due March 6

3/04

Dual of LP. Economics and Pricing Interpretation. Saddle points. Game theory. Duality theory for minimax optimization.

Chapter 5,

Rockafellar: Sec. 33

3/11

Dual of QP. Controllability-observability duality. Dual of $l_p$ optimization. Duality theory for optimization problem with generalized inequality. SDP relaxation.

Chapter 5

HW #3

Due March 21

3/18

Complementary slackness condition. Karush-Kuhn-Tucker (KKT) Conditions. Interpretation of the KKT condition. Regularity condition for local optimality.

Bertsekas Ch. 3

3/25

Algorithms: Descent methods. Newton's method. Equality Constrained Minimization. Infeasible-start Newton's Method. Interior-point method for constrained optimization.

Chapter 9

Chapter 10

Chapter 11

4/01

Interpretation of Interior-point method via KKT condition. Primal-Dual Interior-Point Method. Generalized Inequality. Analytic Centering. Ellipsoid method. Subgradient method for non-differentiable functions. Dual Decomposition. Coordinate descent.

Chapter 11

References:
1, 2, 3

HW #4

Due April 4

Project Report due:

April 6

 4/08

Final Exam: Tuesday April 8, 2025, 9:00am-12noon, BA1170