Topic outline

  • General

    Textbook and Optional References

    •        Stephen Boyd; Lieven Vandenberghe, Convex Optimization (Textbook!)

    •        Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications

    •        Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course

    •        J. Gallier and J. Quaintance, Algebra, Topology, Differential Calculus, and Optimization Theory For Computer Science and Engineering

    Course Requirements and Grading

    Requirements:

    •        4 homework assignments. Homeworks will normally be assigned on Wendsdays and will be due in 2 weeks.

    •        Final Exam. The format will be decided depending on the sitation.

    Grading: 

    Homeworks: 60%. Exam: 40%. These weights are approximate. We reserve the right to change them later. Can be also discussed.

    Description

    Concentrates on recognizing and solving (using standard packages) convex optimization problems that arise in practice!

    •        Convex sets, functions, and optimization problems.

    •        Least-squares, linear and quadratic programs.

    •        Semidefinite programming (SDP).

    •        Minimax, extremal volume, and other problems with geometric interpretation.

    •        Optimality conditions, duality theory, theorem of alternatives.

    •        Introduction to unconstrained optimization algorithms.

    •        Introduction to interior-point methods for constrained optimization.

    •        Applications.

    Course Objectives

    •        to give the tools and training to recognize convex optimization problems that arise in electrical engineering and computer science

    •        to present the basic theory of such problems, concentrating on results that are useful in computations

    •        to give a thorough understanding of how such problems are solved, and some experience in solving them

    •        to give the background required to use the standard methods and software packages (CVX toolbox) in your own research work

    •        to give a number of examples of successful application of convex optimization techniques for solving problem in applied mathematics, computer science, statistics, electrical engineering, and science and engineering in general