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Geometric Optimization


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Geometric optimization problems like computing the smallest ball that contains a given point set (see an example on the left), or the largest ball contained in a polytope, or the distance of two polytopes recently found many applications in machine learning. Most of these optimization problems can be phrased as either a linear program, a convex quadratic program or a semi-definite program. This class covers all three types of optimization problems which themselves have a geometric flavor.

Topics that are covered in this class include:

  • Geometry of Optimization Problems
  • Simplex Method
  • Duality Theory
  • Ellipsoid Method
  • Large Scale Optimization
  • Optimization Algorithms used in Machine Learning

Suggested reading:

  • Dimitris Bertsimas and John N. Tsitsiklis. Introduction to Linear Optimization. Athena Scientific
  • Jiri Matousek and Bernd Gartner. Understanding and Using Linear Programming. Springer Verlag
  • Stephen Boyd and Lieven Vandenberghe. Convex Optimization. Cambridge University Press

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