This website accompanies the paper:

- Gradient descent with nonconvex constraints: local concavity determines convergence.

Rina Foygel Barber and Wooseok Ha. arXiv:1703.07755

This paper studies projected gradient descent over a nonconvex constraint space

*C*. We define the local concavity coefficients of

*C*, measuring the extent to which this set deviates from concavity, and show that these coefficients determine the convergence properties of gradient descent over these constraints. For more information, see the paper.

Here we give code in R to reproduce the empirical results and plots in the paper. The simulated data experiment compares three methods for low-rank matrix estimation: projected gradient descent; gradient descent with approximate projections; and factored gradient descent.

- Simulation script: matrix_simulation.R