ROPTLIB: An Object-Oriented C++ Library for Optimization on Riemannian Manifolds

摘要

Riemannian optimization is the task of finding an optimum of a real-valued function defined 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 processing, 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 article describes ROPTLIB, a C++ library for Riemannian optimization. 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, including quasi-Newton algorithms; and (v) it is based on object-oriented programming, allowing users to rapidly add new algorithms and manifolds.