Hyperbolic Smoothing Method for Sum-Max Problems

Abstract

In this study, an approach for solving non-smooth optimization problem which includes sum of finite maximums of smooth functions is proposed. Minimum l1-norm approximations is a particular case of this problem. In this approach, the problem is reformulated in order to use the hyperbolic smoothing function and the relationship between the original problem and reformulated problem are proved. This approach allows us to use conventional smooth optimization methods. ©Dynamic Publishers, Inc.