An Outer–Inner Linearization Method for Nonconvex and Nondifferentiable Composite Statistical Learning Problems  
Author Minh Pham


Co-Author(s) Xiaodong Lin; Andrzej Ruszczyński


Abstract We propose a new outer–inner lineariztion method for nonconvex statistical learning problems involving nonconvex structural penalties and nonconvex loss. Many important statistical problems fall in this category, including the robust M-estimators, generalized linear models, and different types of structured learning problems. Our method exploits the fact that many such loss and penalty functions can be represented as compositions of smooth concave functions and nonsmooth convex functions. It linearizes the outer concave functions and solves the resulting convex, but still nonsmooth, subproblems by a special alternating linearization method. Numerical examples involving nonconvex structural penalties and nonconvex loss functions demonstrate the efficacy and accuracy of the method.


Keywords Nonsmooth optimization · Nonconvex loss · Nonconvex regularization · Data Mining
    Article #:  DSBFI19-1
Proceedings of ISSAT International Conference on Data Science in Business, Finance and Industry
July 3-5, 2019 - Da Nang, Vietnam