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

References in zbMATH (referenced in 15 articles , 1 standard article )

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  1. Pasadakis, Dimosthenis; Alappat, Christie Louis; Schenk, Olaf; Wellein, Gerhard: Multiway (p)-spectral graph cuts on Grassmann manifolds (2022)
  2. Ronny Bergmann: Manopt.jl: Optimization on Manifolds in Julia (2022) not zbMATH
  3. Yamakawa, Yuya; Sato, Hiroyuki: Sequential optimality conditions for nonlinear optimization on Riemannian manifolds and a globally convergent augmented Lagrangian method (2022)
  4. Seth D. Axen, Mateusz Baran, Ronny Bergmann, Krzysztof Rzecki: Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds (2021) arXiv
  5. Liu, Changshuo; Boumal, Nicolas: Simple algorithms for optimization on Riemannian manifolds with constraints (2020)
  6. Yuan, Xinru; Huang, Wen; Absil, P.-A.; Gallivan, Kyle A.: Computing the matrix geometric mean: Riemannian versus Euclidean conditioning, implementation techniques, and a Riemannian BFGS method. (2020)
  7. Hu, Jiang; Jiang, Bo; Lin, Lin; Wen, Zaiwen; Yuan, Ya-Xiang: Structured quasi-Newton methods for optimization with orthogonality constraints (2019)
  8. Petrosyan, Armenak; Tran, Hoang; Webster, Clayton: Reconstruction of jointly sparse vectors via manifold optimization (2019)
  9. Adragni, Kofi P.: Minimum average deviance estimation for sufficient dimension reduction (2018)
  10. Huang, Wen; Absil, P.-A.; Gallivan, K. A.: A Riemannian BFGS method without differentiated retraction for nonconvex optimization problems (2018)
  11. Huang, Wen; Absil, P.-A.; Gallivan, Kyle A.; Hand, Paul: ROPTLIB: An object-oriented C++ library for optimization on Riemannian manifolds (2018)
  12. Huang, Wen; Hand, Paul: Blind deconvolution by a steepest descent algorithm on a quotient manifold (2018)
  13. Hu, Jiang; Milzarek, Andre; Wen, Zaiwen; Yuan, Yaxiang: Adaptive quadratically regularized Newton method for Riemannian optimization (2018)
  14. Huang, Wen; Gallivan, K. A.; Zhang, Xiangxiong: Solving phaselift by low-rank Riemannian optimization methods for complex semidefinite constraints (2017)
  15. Sean Martin, Andrew M. Raim, Wen Huang, Kofi P. Adragni: ManifoldOptim: An R Interface to the ROPTLIB Library for Riemannian Manifold Optimization (2016) arXiv