Algorithms for large-scale optimal transport

This is a repository of the course project "Algorithms for large-scale optimal transport" for Convex Optimizatin 2018 Fall. It is a group project by Yifei Wang and Feng Zhu (lexicographically).

Numerical experiments

To reproduce the results in our report, please run the following Matlab programs:

• Figure 1 and Figure 2 in Section 3.1.2

  plot_gmm.m

• Figure 3 in Section 4.1.3

  plot_ellipse.m

• Figure 4 in Section 4.1.4

  plot_caff.m

• Perfomance of mosek and gurobi on randomly generated data in Section 4.2.1

  Test_RGD_mb.m

• Perfomance of mosek and gurobi on DOTmark in Section 4.2.2

  Test_DOTmark_mb.m

• Perfomance of mosek and gurobi on Ellipse Example and Caffarelli’s Example in Section 4.2.3

  Test_ellipse_mb.m Test_caff_mb.m

• Perfomance of first order methods on randomly generated data in Section 4.3.2

  Test_RGD_fo.m

• Perfomance of first order methods on DOTmark in Section 4.3.3

  Test_DOTmark_fo.m

• Perfomance of first order methods on Ellipse Example and Caffarelli’s Example in Section 4.3.4

  Test_ellipse_fo.m Test_caff_fo.m

• Figure 5 and Figure 6 in Section 4.4.1

  plot_gmm2.m

• Perfomance of algorithms for entropic regularization of OT on Gaussian mixture model in Section 4.4.1

  Test_gmm_er.m

• Perfomance of algorithms for entropic regularization of OT on randomly generated data in Section 4.4.2

  Test_RGD_er.m

• Perfomance of algorithms for entropic regularization of OT on DOTmark in Section 4.4.3

  Test_RGD_er.m

• Perfomance of algorithms for entropic regularization of OT on Ellipse Example and Caffarelli’s Example in Section 4.4.4

  Test_ellipse_er.m Test_caff_er.m

Explanation of our codes

Model

'model_*.m' generates an OT model based on different dataset and 'model_unified.m' is a unified program to generate OT models.

LP/LPER

'LP_*.m' implements different algorithms to solve the LP problem.

'LPER_*.m' implements different algorithms to solve the entropic regularization of OT.

OT

'OT_*.m' provides necessary functions to create an OT model.

Plot

'Plot_*.m' plots figures in our reports.

Test

'Test_*.m' implements numerical experiments in our reports.