Software

Software and solvers by Zhijian Lai

Solvers for Manifold Optimization

Although Manopt is a widely used Riemannian manifold solver, some problems require nonsmooth objectives or additional constraints. The following projects extend this direction.

RieSmooth: nonsmooth objectives on Riemannian manifolds

RieSmooth is a general Riemannian smoothing algorithm for nonsmooth Riemannian optimization problems

min x \in M f(x)

where $M$ is any available manifold in Manopt, and $f: M \to R$ is nonsmooth.

Code and Instructions

Reference: Zhijian Lai, Akiko Yoshise. Completely positive factorization by a Riemannian smoothing method. Computational Optimization and Applications, 83, 933–966, 2022. https://doi.org/10.1007/s10589-022-00417-4

Examples include completely positive matrix factorization (CPfact), finding the sparsest vector in a subspace (FSV), and robust low-rank matrix completion (RMC).

RIPM: additional constraints on Riemannian manifolds

Riemannian Interior Point Methods (RIPM) is a primal-dual interior point solver for nonlinear optimization problems on Riemannian manifolds with equality and inequality constraints:

min x \in M f(x) s.t. h(x) = 0, g(x) \leq 0,

where $M$ is any available manifold in Manopt, and $f: M \to R$ , $h: M \to R l$ , and $g: M \to R m$ are smooth.

Code and Instructions Manopt.jl Implementation

Reference: Zhijian Lai, Akiko Yoshise. Riemannian Interior Point Methods for Constrained Optimization on Manifolds. Journal of Optimization Theory and Applications, 201, 433–469, 2024.