Definition

Manifold optimization is concerned with the optimization problem

\min_{x \in \mathcal{M}}\quad f(x)$$ where $\mathcal{M}$ is a [[Riemannian manifold]] and $f$ is a real-valued function on $\mathcal{M}$, which can be non-[[smooth function|smooth]]. --- ## References 1. J. Hu, X. Liu, Z.-W. Wen, and Y.-X. Yuan, “A Brief Introduction to Manifold Optimization,” _J. Oper. Res. Soc. China_, vol. 8, no. 2, pp. 199–248, Jun. 2020, doi: [10.1007/s40305-020-00295-9](https://doi.org/10.1007/s40305-020-00295-9). ParseError: Can't use function '$' in math mode at position 35: …l{M}}\quad f(x)$̲$ where $\mathc…