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Approximating Concavely Parameterized Optimization Problems

2020-01-13 | |  87 |   34 |   0

Abstract

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 图片.png > 0 by a set of size 图片.png A lower bound of size 图片.png 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 图片.png Finally, we provide an implementation of the oracle for soft-margin support vector machines, and a parameterized semi-definite program for matrix completion.

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