Riemannian Interior Point Methods (RIPM) for Constrained Optimization on Manifolds
This is a primal-dual interior point methods solver for nonlinear optimization problems on Riemannian manifolds, which aims to minimize the cost function in the given problem structure with (in)equality constraints
For a description of the algorithm and theorems offering convergence guarantees, see the references:
Z. Lai and A. Yoshise. Riemannian Interior Point Methods for Constrained Optimization on Manifolds. [arXiv]
We prepared a additional document Implement Note of Global RIPM with detailed instructions for the implementation.
[New!] We upload a new tutorial for quick start.
The codes below correspond to the Numerical Experiments Section in the paper.
By running the Boss_*.m files, the numerical experiments are executed with the same settings as in the paper. The results will be output in csv format in the .\numerical results folder. Note: It may take 1-2 days to run the full experiment through the .\bosses\cmd.m file.
| MATLAB code (.\bosses\) | Corresponding questions in our paper |
|---|---|
| Boss_1_fixedrank_NLRM.m | Problem I (NLRM) |
| Boss_2_Stiefel_NonnegativeProjection.m | Problem II (Model_St) |
| Boss_3_Ob_equality_NonnegativeProjection.m | Problem II (Model_Ob) |
The corresponding client_*.m files combines specific problems with various solvers. They are used in the Boss_*.m files.
| MATLAB code (.\clients\) | Corresponding questions in our paper |
|---|---|
| client_fixedrank_NLRM.m | Problem I (NLRM) |
| client_Stiefel_NonnegativeProjection.m | Problem II (Model_St) |
| client_Ob_equality_NonnegativeProjection.m | Problem II (Model_Ob) |
The codes below do not appear in the paper and are used to test various example problems for our RIPM.
| MATLAB code (.\examples\) | M | f | g | h |
|---|---|---|---|---|
| Euc_linear_nonnega_sphereEq | Euclidean | linear | nonnegative | sphere x'*x=1 |
| Euc_linear_or_projection_nonnega_orthogonalEq | Euclidean | linear/projection | nonnegative | orthogonality X'*X-I=0 |
| Euc_projection_nonnega | Euclidean | projection | nonnegative | - |
| Euc_projection_nonnega_symmetricEq | Euclidean | projection | nonnegative | symmetry X-X'=0 |
| Fixedrank_MatrixCompletion_nonnega | fixedrank | matrix completion | nonnegative | - |
| Fixedrank_MatrixCompletion_nonnega_reliableEq | fixedrank | matrix completion | nonnegative | reliable sampled data |
| Fixedrank_projection_nonnega | fixedrank | projection | nonnegative | - |
| Ob_ONMF_StiefelEq | oblique | -trace(X'AAtX) | nonnegative | norm(X*V,'fro')^2-1 |
| Ob_linear_or_projection_nonnega_StiefelEq | oblique | linear/projection | nonnegative | norm(X*V,'fro')^2-1 |
| Sp_linear_nonnega | sphere | linear | nonnegative | - |
| Sp_linear_nonnega_linearEq | sphere | linear | nonnegative | linear |
| Sp_quadratic_nonnega | sphere | quadratic | nonnegative | - |
| Stiefel_linear_or_projection_nonnega | stiefel | linear/projection | nonnegative | - |
| Sym_projection_nonnega | symmetric | projection | nonnegative | - |
| run_all_examples |