Contents:

      Intro

      Code





Intro


This website accompanies the paper:
  • MOCCA: mirrored convex/concave optimization for nonconvex composite functions.
    Rina Foygel Barber and Emil Y. Sidky. To appear in Journal of Machine Learning Research. arXiv:1510.08842

Our paper proposes an algorithm for minimizing a nonconvex composite function of the form F(Kx)+G(x), where F and G may be nonconvex and/or nondifferentiable and K is a known linear transformation. The method is a primal/dual algorithm where, at each iteration, we take a local convex approximation to F and to G; since we work with F in the dual space, the approximation to F is taken at a point that mirrors the dual variable.

The algorithm was initially designed for the problem of image reconstruction with spectral CT (computed tomography) imaging, and is implemented for the CT problem in the paper:
  • An algorithm for constrained one-step inversion of spectral CT data.
    Rina Foygel Barber, Emil Y. Sidky, Taly Gilat Schmidt, Xiaochuan Pan. arXiv:1511.03384

Here are some slides presenting work from both papers.






Code


Here we provide MATLAB code for reproducing the two simulations in the MOCCA paper. Simulation 1 (nonconvex total variation penalty): this simulation compares two different implementations of MOCCA for a least squares regression problem with a nonconvex total variation penalty. The objective function is therefore a convex loss function plus a nonconvex penalty.
Simulation 2 (errors in variables with a total variation penalty): this simulation compares MOCCA against proximal gradient descent for a least squares regression problem with a (convex) total variation penalty, where only noisy versions of the regression variables are available. The objective function is therefore a nonconvex loss function plus a convex penalty.