Approximating Parameterized Convex Optimization Problems

  • Joachim Giesen
  • Martin Jaggi
  • Sören Laue
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6346)


We extend Clarkson’s framework by considering parameterized convex optimization problems over the unit simplex, that depend on one parameter. We provide a simple and efficient scheme for maintaining an ε-approximate solution (and a corresponding ε-coreset) along the entire parameter path. We prove correctness and optimality of the method. Practically relevant instances of the abstract parameterized optimization problem are for example regularization paths of support vector machines, multiple kernel learning, and minimum enclosing balls of moving points.


Support Vector Machine Solution Path Parameter Interval Multiple Kernel Learning Approximation Guarantee 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Joachim Giesen
    • 1
  • Martin Jaggi
    • 2
  • Sören Laue
    • 1
  1. 1.Friedrich-Schiller-Universität JenaGermany
  2. 2.ETH ZürichSwitzerland

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