Approximating parameterized convex optimization problems

Joachim Giesen, Martin Jaggi, Sören Laue

Abstract: We consider 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.