Convex Optimization - Fall, 2017
This course provides an overview of topics in convex optimization, a sub-area of optimization that studies the problem of optimizing convex functions over convex sets. The convexity makes optimization easier than the general case since a local optimum must necessarily coincide with the global optimum, and first-order conditions are sufficient conditions for optimality. This graduate course introduces the basic theory and illustrates its use with some recent applications in computer networks and wireless communication systems. Special attention will be given to: i) the techniques for uncovering the hidden convexity of problems by appropriate manipulations, and ii) a proper characterization of the solution either analytically or algorithmically.
Term: FAll Quarter, 2017
Lecture: Sun and Tue, 15:30-17:00
Main Text: S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004, ISBN: 0521833787
Syllabus: [pdf]
Lectures
- Lecture 0 - Course Introduction: [pdf]
- Lecture 1 - Efficiency, Parteo-Optimality, and Fairness: [pdf]
- Lecture 2 - Introduction to Convex Programming: [pdf]
- Lecture 3 - Convex Sets: [pdf]
- Lecture 4 - Convex Functions: [pdf]
- Lecture 5 - Optimization Basics: [pdf]
- Lecture 6 - Canonical Problem Forms: [pdf]
- Lecture 7 - Gradient Descent: [pdf]
- Lecture 8 - Sub-gradients and the Sub-gradient Method: [pdf]
- Lecture 9 - Introduction to Duality: [pdf]
- Lecture 10 - Karush-Kuhn-Tucker (KKT) Conditions: [pdf]
- Lecture 11 - Introduction to Pricing Mechanisms: [pdf]