# EE227A PROJECTS

## 1 INTRODUCTION

One of the most important components of EE227A is a class project. The aim of the project is to foster research, implementation, and experimental validation, along with writing of a high quality project paper. To ease the burden, your EE227A class project can overlap with your research agenda, and if needed with a class project for some other class—however, in the latter case, it cannot be exactly the same project, because you must emphasize the role of optimization in the EE227A project.

### 1.1 ORGANIZATION

The project timeline is as follows:

**OUTLINE / PROPOSAL**

This part requires you to submit a**1 page**outline of the project topic, names of team members, and a brief description of how you plan to solve the problem. Include background information, and references.**[**]

**MIDTERM REPORT**

This report is due on

**[**. It includes a ]**4 page**writeup that includes a clear problem statement (mathematical model), and some initial results. This report will be reviewed by your peers.

**PEER REVIEW**

Each project team will have to review a midterm progress report submitted by another team. You'll provide clear, constructive feedback (anonymously), of max

**1 page**length, and this feedback will be sent to the other team.**[**]

**POSTER PRESENTATION**

Details to be decided; you'll present your work as a poster during a combined poster session (3-4 hours long on some evening); this should make for an exciting "mini-conference" like feel.

**FINAL PAPER**

A final project report / paper written in standard conference paper style should be submitted. Discuss this with your instructor or TAs in case you have any questions. Maximum length of main paper**8 pages**; feel free to provide an online supplement to your paper (the supplement will not be graded, but will help you maintain complete details of your project for future reference).**[**]**NOTE:**The deadline corresponds to the latest date by which you may submit the project; this date corresponds to the official day our final exam would have been, had we chosen to have one. If you finish before this deadline, that is perfectly fine too.We'll provide a LaTeX template (on bSpace) for typesetting your final project report.

Projects will roughly fall under the following five broad areas: (i) literature review; (ii) theory; (iii) algorithms and models; (iv) applications; and (v) software.

## 2 PROJECT SUGGESTIONS

### 2.1 LITERATURE REVIEW

- Make a brief survey of methods for solving the minimum volume ellipsoind (enclosing, covering, etc) problem
- Summarize the key papers related to the Douglas-Rachford method (including the more recent papers that discuss convergence rate)

### 2.2 THEORY

- OPEN PROBLEMS

- Prove log-convexity of \(\frac{\sigma_{n+1}(x)}{\sigma_n(x)}\), where \(\sigma_n(x) = 1^x+2^x+\cdots+n^x\)
- Douglas-Rachford for \(f(x) + g(x)\) where \(f\) is nonconvex
- Study convergence properties of ADMM with 3 (or more) terms.
- Investigate challenge problem mentioned in lecture 5

- OTHER THEORY PROBLEMS

### 2.3 ALGORITHMS & PROBLEMS

- Solver for \(f(x) + \lambda \|Bx\|\)
- Algorithm for \(f(x) + \sum_i r_i(x)\), where \(r_i\) are nonsmooth, convex
- Convex relaxations for approximately solving norm(A-uu') over u >= 0
- Solve separable convex s.t. almost separable block linear constraints
- Solve the matrix balancing via optimization
- Finding nearest doubly stochastic matrix

- Investigate Conditional gradient methods for norm regularized problems
- Investigate conditional gradient methods for norm constrained problems
- Investigate the spectral projected gradient method (Barzilai-Borwein)

### 2.4 APPLICATION AREAS

- Geometric programming problems in algebraic geometry
- Machine learning
- Learning Mahalanobis metrics
- Learning Similarity functions

- Computational photography
- Solving blind deconvolution via SDPs
- Look at ICCP 2012 (ICCP 2012 Website)

- System identification
- Computer vision
- Wireless sensor placement
- Portfolio optimization
- Portfolio optimization with sparsity constraints

- Dictionary learning (see Workshop on DL)

### 2.5 SYSTEMS AND SOFTWARE

- Implement solver (Matlab or Python) for the generalized trust-region subproblem
- Large-scale linear programming solver (via augmented lagrangian methods)
- Large-scale linear programming solver via this nice paper!
- Implement a distributed matrix factorization
- Implement a well-tuned version of FISTA (with improvements to stepsize tuning)