Optimization Lab for Communication and Signal Processing Using MATLAB (OptiLab)

This Lab is about learning how to recognize, model and solve optimization problems. Covered topics include but are not limited to:

Linear Programming
Quadratic Programming and Least-Squares Problems
Regularized Approximation and Estimation
Second-order Cone Programming
Semidefinite Programming
Methodologies to solve a convex problem
Theoretical analysis
- Duality theory, Karush-Kuhn-Tucker (KKT) conditions of optimality
Numerical approach
- CVX: Matlab Toolbox for convex optimization problems
- Numerical solvers for convex problems: e.g., SeDuMi, SDPT3
Application to a wide range of topics, e.g.
- Healthy diet problems (what foods to eat and how much)
- Network Optimization: Minimum cost network flow problem, Max-flow min-cut problem
- Communication systems: Chebyshev bounds on probability of symbol detection
- Data analysis and synthesis
  - Sparse signal recovery and compressed sensing
  - Outlier identification
  - Data smoothing

Reading assignments

In each session, you will receive a reading assignment (from 5 to 20 pages) for the subsequent session. At the beginning of each session, there will be a multiple choice test to check if you read and understood the material covered in the reading assignment.

4 | Linear Programming II

You will need the Matlab function combn, which you can find at the Mathworks website:

[combn]

and the following template files (right-click, save as):

[s4p1c_template.m] and [s4p1fg_template.m].

5 | Quadratic Programming

You will need the following files (right-click, save as):

[s5p1a_template.m], [s5p1d1_template.m], [s5p1d2_template.m], [s5p1e_template.m] and [data_problem_1.mat].

6 | Duality

You will need the following files (right-click, save as):

[s6p1a_template.m], [s6p1d_template.m] and [s6p1_params_template.m]

7 | Approximation, vector optimization and regularization