Convex-Concave Backtracking for Inertial Bregman Proximal Gradient Algorithms in Non-Convex Optimization
by Mahesh Chandra Mukkamala, Peter Ochs, Thomas Pock and Shoham Sabach.
CoCaIn BPG escapes Spurious Stationary Points
CoCaIn BPG for Matrix Factorization
BPG: Bregman Proximal Gradient (BPG)
CoCaIn BPG: Convex Concave Inertial (CoCaIn) BPG
BPG-WB: BPG with Backtracking
IBPM-LS: Inexact Bregman Proximal Minimization Line Search Algorithm
- numpy, matplotlib
If you have installed above mentioned packages you can skip this step. Otherwise run (maybe in a virtual environment):
pip install -r requirements.txt
To generate results
chmod +x generate_results.sh
./generate_results.sh
Then to create the plots
chmod +x generate_plots.sh
./generate_plots.sh
Now you can check figures folder for various figures.
The function number is denoted as fun_num.
In fun_num 1 : L1-Regularization is used.
In fun_num 2 : Squared L2-Regularization is used.
@techreport{MOPS19,
title = {Convex-Concave Backtracking for Inertial Bregman Proximal Gradient Algorithms in Non-Convex Optimization},
author = {M.C. Mukkamala and P. Ochs and T. Pock and S. Sabach},
year = {2019},
journal = {ArXiv e-prints, arXiv:1904.03537},
}
Mahesh Chandra Mukkamala (mukkamala@math.uni-sb.de)
M. C. Mukkamala, P. Ochs, T. Pock, and S. Sabach: Convex-Concave Backtracking for Inertial Bregman Proximal Gradient Algorithms in Non-Convex Optimization. ArXiv e-prints, arXiv:1904.03537, 2019.
P. Ochs, J. Fadili, and T. Brox. Non-smooth Non-convex Bregman Minimization: Unification and New Algorithms. Journal of Optimization Theory and Applications, 181(1):244–278, 2019.
J. Bolte, S. Sabach, M. Teboulle, and Y. Vaisbourd. First Order Methods Beyond Convexity and Lipschitz Gradient Continuity with Applications to Quadratic Inverse Problems. SIAM Journal on Optimization, 28(3):2131–2151, 2018.