ROPTLIB: an object oriented C++ library for optimization on Riemannian manifolds

Wen Huang, P.-A. Absil, K. A. Gallivan, Paul Hand

Riemannian optimization is the task of finding an optimum of a real-valued function de- fined on a Riemannian manifold. Riemannian optimization has been a topic of much interest over the past few years due to many applications including computer vision, signal process- ing, and numerical linear algebra. The substantial background required to successfully design and apply Riemannian optimization algorithms is a significant impediment for many potential users. Therefore, multiple packages, such as Manopt (in Matlab) and Pymanopt (in Python), have been developed. This paper describes ROPTLIB, a C++ library for Riemannian opti- mization. Unlike prior packages, ROPTLIB simultaneously achieves the following goals: i) it has user-friendly interfaces in Matlab, Julia and C++; ii) users do not need to implement manifold- and algorithm-related objects; iii) it provides efficient computational time due to its C++ core; iv) it implements state-of-the-art generic Riemannian optimization algorithms, in- cluding quasi-Newton algorithms; and v) it is based on object-oriented programming, allowing users to rapidly add new algorithms and manifolds. The code and a manual can be downloaded from