EE227A PROJECTS

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. [ DEADLINE: 2013-03-14 Thu]

• MIDTERM REPORT
  

  This report is due on [ 2013-04-11 Thu]. 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. [ DEADLINE: 2013-04-18 Thu]

• 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). [ DEADLINE: 2013-05-16]

  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.

• 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)

• 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
  

• 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)

• 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)

• 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)