Convex Optimization has become more and more important to people researching machine learning.

Stephen Boyd has a series of video lectures available on this topic.

The video lectures are in two parts: "Convex Optimization I" and "Convex Optimization II". Here is the description of the "Convex Optimization I" sub-series:

Convex Optimization I 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.

And here is the description for the "Convex Optimization II" sub-series:

This course introduces topics such as subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Alternating projections. Exploiting problem structure in implementation. Convex relaxations of hard problems, and global optimization via branch & bound. Robust optimization. Selected applications in areas such as control, circuit design, signal processing, and communications.

All video below:

• Lecture 1: Convex Optimization I
• Lecture 2: Convex Optimization I
• Lecture 3: Convex Optimization I
• Lecture 4: Convex Optimization I
• Lecture 5: Convex Optimization I
• Lecture 6: Convex Optimization I
• Lecture 7: Convex Optimization I
• Lecture 8: Convex Optimization I
• Lecture 9: Convex Optimization I
• Lecture 10: Convex Optimization I
• Lecture 11: Convex Optimization I
• Lecture 12: Convex Optimization I
• Lecture 13: Convex Optimization I
• Lecture 14: Convex Optimization I
• Lecture 15: Convex Optimization I
• Lecture 16: Convex Optimization I
• Lecture 17: Convex Optimization I
• Lecture 18: Convex Optimization I
• Lecture 19: Convex Optimization I

• Lecture 1: Convex Optimization II
• Lecture 2: Convex Optimization II
• Lecture 3: Convex Optimization II
• Lecture 4: Convex Optimization II
• Lecture 5: Convex Optimization II
• Lecture 6: Convex Optimization II
• Lecture 7: Convex Optimization II
• Lecture 8: Convex Optimization II
• Lecture 9: Convex Optimization II
• Lecture 10: Convex Optimization II
• Lecture 11: Convex Optimization II
• Lecture 12: Convex Optimization II
• Lecture 13: Convex Optimization II
• Lecture 14: Convex Optimization II
• Lecture 15: Convex Optimization II
• Lecture 16: Convex Optimization II
• Lecture 17: Convex Optimization II
• Lecture 18: Convex Optimization II

A play list is available too.

-- Charles Iliya Krempeaux