Convex Optimization II

Textbook and optional references

The textbook is Convex Optimization, available online, or in hard copy form at the Stanford Bookstore.

Several texts can serve as auxiliary or reference texts:

• Bertsekas, Nedic, and Ozdaglar, Convex Analysis and Optimization
• Ben-Tal and Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications
• Nesterov, Introductory Lectures on Convex Optimization: A Basic Course
• Ruszczynski, Nonlinear Optimization
• Borwein & Lewis, Convex Analysis and Nonlinear Optimization

Description

Continuation of 364a. 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. Course requirements include a substantial project.

Lecture Slides and Notes

Professor Stephen Boyd, Stanford University

Lecture slides:

1. Subgradients (notes)
2. Subgradient methods (notes | matlab files)
3. Subgradient methods for constrained problems
4. Stochastic subgradient method (notes | matlab files)
5. Localization and cutting-plane methods (notes)
6. Analytic center cutting-plane method (notes | matlab files)
7. Ellipsoid method (matlab files)
8. Primal and dual decomposition (notes | matlab files)
9. Decomposition applications
10. Sequential convex programming (matlab files)
11. Conjugate-gradient method (matlab files)
12. Truncated Newton methods (matlab files)
13.  methods for convex-cardinality problems (matlab files)
14.  methods for convex-cardinality problems, part II (matlab files)
15. Model predictive control (matlab files)
16. Stochastic model predictive control
17. Branch-and-bound methods (notes | python files)

Additional lecture notes:

1. Notes on relaxation and randomized methods for nonconvex QCQP
2. Sum-of-squares (SOS) methods
3. Notes on convex-concave games and minimax
4. Numerical linear algebra software

Lecture Videos

Professor Stephen Boyd, Stanford University

Lecture	Slides
Apr 1	Subgradients	Flash	iTunes
Apr 3	Subgradients, subgradient methods	Flash	iTunes
Apr 8	Subgradient methods for constrained problems	Flash	iTunes
Apr 10	Stochastic subgradient methods	Flash	iTunes
Apr 15	Localization methods	Flash	iTunes
Apr 17	Analytic center cutting-plane method	Flash	iTunes
Apr 22	Ellipsoid method	Flash	iTunes
Apr 24	Ellipsoid method, decomposition	Flash	iTunes
Apr 29	Primal and dual decomposition	Flash	iTunes
May 1	Decomposition applications	Flash	iTunes
May 6	Sequential convex programming	Flash	iTunes
May 8	Conjugate-gradient method	Flash	iTunes
May 13	Truncated Newton method	Flash	iTunes
May 15	methods	Flash	iTunes
May 20	methods	Flash	iTunes
May 22	Model predictive control	Flash	iTunes
May 27	Stochastic model predictive control	Flash	iTunes
May 29	Branch and bound	Flash	iTunes