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Approximating Concavely Parameterized Optimization Problems
Joachim Giesen · Jens K Mueller · Soeren Laue · Sascha Swiercy

Tue Dec 04 03:10 PM -- 03:30 PM (PST) @ Harveys Convention Center Floor, CC
We consider an abstract class of optimization problems that are parameterized concavely in a single parameter, and show that the solution path along the parameter can always be approximated with accuracy $\varepsilon >0$ by a set of size $O(1/\sqrt{\varepsilon})$. A lower bound of size $\Omega (1/\sqrt{\varepsilon})$ shows that the upper bound is tight up to a constant factor. We also devise an algorithm that calls a step-size oracle and computes an approximate path of size $O(1/\sqrt{\varepsilon})$. Finally, we provide an implementation of the oracle for soft-margin support vector machines, and a parameterized semi-definite program for matrix completion.

Author Information

Joachim Giesen (Friedrich-Schiller-Universitat Jena)
Jens K Mueller (Friedrich Schiller University Jena)
Soeren Laue (Friedrich Schiller University Jena / Data Assessment Solutions)
Sascha Swiercy (Friedrich-Schiller-Universität Jena)

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