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Convex Optimization


Convex optimization studies the problem of minimizing a convex function over a convex domain. It is one of the fundamental branches of computer science and mathematics. Many real world problems  like portfolio optimization, data fitting problems, or production planning can be phrased as a convex optimization problem. This class focuses on the theoretical background, algorithms, and practical implementation issues. Especially convex optimization problems arising in machine learning will serve as examples.  A solid mathematical background is suggested. The class will consist of a theory part and a practical part where the algorithms will have to be implemented in either C++ or Matlab.

This course can be taken as a bachelor course as well as a master course.

Topics that are covered in this class include:

  • Geometry of Convex Optimization Problems
  • Duality Theory
  • Lower Bounds
  • Algorithms (Subgradient Methods, Gradient Methods, Interior Point Methods)
  • Large Scale Optimization
  • Optimization Algorithms used in Machine Learning

Suggested reading:

  • Stephen Boyd and Lieven Vandenberghe. Convex Optimization. Cambridge University Press. (also available as PDF here)
  • Yurii Nesterov. Introductory Lectures on Convex Optimization. Kluwer Academic Publishers.
  • Jorge Nocedal and Stephen J. Wright. Numerical Optimization. Springer.

Please register for this class through CAJ (only for registered users).