Professor Stephen Boyd, of the Stanford University Electrical Engineering department, lectures on the different problems that are included within convex optimization for the course, Convex Optimization I (EE 364A).

1. Introduction
2. Convex Sets
3. Convex and Concave Functions
4. Convex Functions in Electrical Engineering
5. Convex Optimization Problems
6. Convex Optimization Problems (cont.)
7. Convex Optimization Problems (cont.)
8. Duality in Electrical Engineering
9. Duality in Electrical Engineering (cont.)
10. Approximation and Fitting Within Convex Optimization
11. Statistical Estimation
12. Geometric Problems
13. Geometric Problems (cont.)
14. Numerical Linear Algebra
15. Unconstrained Minimization in Electrical Engineering
16. Equality Constrained Minimization in Electrical Engineering
17. Equality Constrained Minimization in Electrical Engineering (cont.)
18. Interior-Point Methods of Electrical Engineering
19. Final Lecture

Concentrates on recognizing and solving convex optimization problems that arise in engineering. Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interior-point methods. Applications to signal processing, control, digital and analog circuit design, computational geometry, statistics, and mechanical engineering.

Tags: Math, Math Convex