In 2006-07, EE392 was turned into a permanent course, EE364b: Convex Optimization II.

**Introduction.**Structure of course, student requirements, timeline. About the project; ideas for projects.**Subgradients.**Basics of subgradients and the subdifferential. Subgradient calculus, examples. Optimality conditions for nondifferentiable problems. Relation to directional derivative.**Localization methods**. Basic idea of localization and cutting-plane methods. CG method, ACCPM. Notes on localization and cutting-plane methods.**Ellipsoid method**.**Subgradient methods.**Subgradient method with fixed and diminishing step lengths. Convergence theorems and proofs. Projected subgradient method. Example: Decentralized dual algorithm for optimal network flow. Notes on subgradient methods.**Primal and dual decomposition.**Primal and dual decomposition for decentralized, distributed methods. Notes on decomposition methods. Decomposition method example (slides).**Alternating projections.**Alternating projections and extensions. Convergence results and proofs. Examples. Notes on alternating projections. Alternating projections example (slides).**Numerical linear algebra.**Covers material in Appendix C of Boyd and Vandenberghe.**Numerical linear algebra software.**Practical aspects and issues. BLAS levels I, II, III; ATLAS. LAPACK. Sparse packages. Notes on numerical linear algebra software.**Convex/concave games.**Matrix games, mixed strategies, maxmin theorem, solution via LP. Bilinear polyhedral games; robust LP example. Continuous convex-concave games, maxmin theorem, transforming to minmin via duality. Numerical methods for convex-concave games: Newton's method; barrier method. Example: minimax power allocation in wireless system. Notes on convex-concave games and minimax.**Branch-and-bound methods.**Branch-and-bound, global optimization, integer programming. Notes on branch and bound methods. Notes on branch and bound methods (slides).**Relaxation methods for nonconvex QCQP.**SDP and Lagrangian relaxations; connection to randomized algorithms. Notes on relaxation and randomized methods for nonconvex QCQP..**Robust optimization.**Lecture by Professor Laurent El Ghaoui.**Convex optimization in classification problems.**Lecture by Professor Laurent El Ghaoui.**Sum-of-squares (SOS) relaxations for hard problems.**Lecture by Professor S. Lall.**Convex optimization applications in signal processing.**Lecture by Professor Z.-Q. Luo. Interior-point optimization techniques for adaptive filtering.**Convex optimization applications in communications.**Lecture by Professor Z.-Q. Luo. Minimum BER linear transceivers for block communication systems.**SDP for Euclidean distance geometric optimization.**Ad hoc wireless network sensor location. Euclidean ball packing. Lecture by Professor Yinyu Ye.**Convex optimization applications in communications.**Lecture by Professor Z.-Q. Luo. Optimal tranceiver design for multi-access communication.

**Dec. 4th, Thursday:**

- 1:00-1:30 pm: Vivek Farias (Scheduling Projects with Shared Resources)
- 1:30-2:00 pm: Ritesh Madan (A Distributed Algorithm for Maximum Lifetime Routing in Ad Hoc Wireless Networks)
- 2:00-2:30 pm: Erik Stauffer (Maximizing Outage Capacity)
- 2:30-3:00 pm: Unscheduled

**Dec. 11th, Thursday, Session 1 (Packard 277):**

- 10:00-10:30 am: Elad Alon and Vladimir Stojanovic (Optimal Utilization of Multi-mode Fiber for Optical Communications)
- 10:30-11:00 am: Randy Cowgill (Convex Relaxations for Decentralized Decision Problems)
- 11:00-11:30 am: Eunchul Yoon and Taesang Yoo (Optimal Linear pre-coder and Power Allocation for MIMO-OFDM Systems with Partial and Imperfect Channel Knowledge)
- 11:30-12:00 pm: Amal Ekbal (Distributed Power Control in Multiple Antenna Wireless Networks)
- 12:00-12:30 pm: Jun Sun and Arpita Ghosh (Eigenvalue Optimization for Laplacian Matrices of Graphs)

**Dec. 11th, Thursday, Session 2 (Packard 277):**

- 2:00-2:30 pm: Christopher Gadda (Optimal Grasp Selection for Climbing Robots)
- 2:30-3:00 pm: Alok Agarwal (Minimization of PAPR in OFDM Systems)
- 3:00-3:30 pm: Sunghee Yun and Dinesh Patil (Optimal Sizing of Digital Circuits via Statistical Problem Formulation using Generalized Geometric Programming)
- 3:30-4:00 pm: Almir Mutapcic and Majid Emami (Dynamic Routing with Active Queue Management)

**Dec. 12th, Friday, Session 1 (Packard 277) :**

- 10:00-10:30 am: Ramesh Kumar and Joy Rajiv (Option Pricing Based on Dual Underlying Assets Using Convex Optimization)
- 10:30-11:00 am: Mehdi Mohseni (Sub-optimal Throughput Maximization Schemes for Vector Broadcast Channels)
- 11:00-11:30 am: Mayank Sharma
- 11:30-12:00 pm: Alessandro Magnani (Maximum a-posteriori Probability Estimation of Sigma-Delta Raw Data)

**Dec. 11th, Friday, Session 2 (Packard 277):**

- 2:00-2:30 pm: Robin Raffard (Decentralized Control of Multiple Vehicle Systems using Convex Optimization)
- 2:30-3:00 pm: Kaustuv (Exploiting Sparsity in the Dual-Scaling Method for Semidefinite Programs via Automatic Differentiation of the Logarithmic Barrier Function
- 3:00-3:30 pm: Mark Brady (The Worst-case Interference in DSL Systems Employing Dynamic Spectral Management)
- 3:30-4:00 pm: Sina Zahedi (Gaussian Channel Capacity with Feedback)

**Credit:** 3 units.

**Lectures:** Tuesdays and Thursdays, 1:15-2:30, location
380-380D.

**Instructors:**

- Professor Stephen
Boyd, Packard 264, (650) 723-0002,
`boyd@stanford.edu`. Office hours: Wednesdays 9:30-11:30. - Professor
Z.-Q. Luo, Packard 253, (650) 724-6783,
`luozq@ece.umn.edu`. Professor Luo is an ISL visitor from ECE Dept., Univ. of Minnesota, and will be giving several guest lectures. His McMaster Unversity website has more information than his Univ. of Minnesota page.

**Administrative assistant:**
Denise Murphy,
Packard 267, 723-4731, Fax 723-8473,
`denise@ee.stanford.edu`

**Teaching Assistants:**

**TA office hours & location:** Monday 4pm to 6pm and
Friday 5pm to 6pm in Packard 242

**Textbook:**
*Convex
Optimization*, S. Boyd and L. Vandenberghe, Cambridge
University Press 2003.

**Course requirements:** There will be no homework or exams;
the only formal requirement is a substantial class project. Class
attendance (within reason) is also required.

**Prerequisite:** EE364 or consent of instructor.