Abstract
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.
This work has been supported by the DFG under grant GI-711/3-1, by a Google Research Award, and by the Swiss National Science Foundation (SNF Project 20PA21-121957).
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Giesen, J., Jaggi, M., Laue, S. (2010). Approximating Parameterized Convex Optimization Problems. In: de Berg, M., Meyer, U. (eds) Algorithms – ESA 2010. ESA 2010. Lecture Notes in Computer Science, vol 6346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15775-2_45
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DOI: https://doi.org/10.1007/978-3-642-15775-2_45
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