Grading
  • 55% homeworks, 35% final project, 10% participation (tentative)
Homework
  • Weekly homework assignments (8 homework sets), which involve some MATLAB programming. There will be a Final Project, and no final exam.
Course Description
The course concentrates on recognizing and solving convex optimization problems that arise in engineering and sciences. Syllabus includes:
  • Basics of convex analysis: Convex sets, functions, and optimization problems.
  • Optimization theory: Least-squares, linear, quadratic, geometric and semidefinite programming, and other problems. Optimality conditions, duality theory, and applications.
  • Application examples from signal processing, control, communications, statistics, networks, finance and economics, engineering design.
Course Objectives
  • to give students the theoretical tools and training to recognize convex optimization problems,
  • to present the underlying theory of such problems, concentrating on mathematical results that are useful in computation,
  • to give students experience in solving these problems, and the background required to use the methods in their own research work.
Textbook and Optional References (reserved in the Engineering Library)
The main textbook is

Optional books that serve as secondary references:

General

  • A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications. MPS/SIAM Series on Optimization.
Theory
  • D. Bertsekas, A. Nedic, A. Ozdaglar, Convex Analysis and Optimization. Athena Scientific.
  • D. Bertsekas, Convex Optimization Theory. Athena Scientific.
  • J. Borwein, A. Lewis, Convex Analysis and Nonlinear Optimization: Theory and Examples. Springer-Verlag.
  • D. Luenberger, Linear and Nonlinear Programming, Addison-Wesley.
Algorithms
    We won't cover algorithms in this course, but here's a good book:
  • J. Nocedal and S. Wright, Numerical Optimization, Springer.