Nonsmooth DC programming approach to clusterwise linear regression: optimality conditions and algorithms

© 2017 Informa UK Limited, trading as Taylor & Francis Group. The clusterwise linear regression problem is formulated as a nonsmooth nonconvex optimization problem using the squared regression error function. The objective function in this problem is represented as a difference of convex functions. Optimality conditions are derived, and an algorithm is designed based on such a representation. An incremental approach is proposed to generate starting solutions. The algorithm is tested on small to large data sets.