Riemannian Conjugate Gradient Methods: General Framework and Specific Algorithms with Convergence Analyses

Sequential optimality conditions for nonlinear optimization on Riemannian manifolds and a globally convergent augmented Lagrangian method

(2022) Yuya Yamakawa et al.   COMPUTATIONAL OPTIMIZATION AND APPLICATIONS

Fenchel Duality Theory and a Primal-Dual Algorithm on Riemannian Manifolds

(2021) Ronny Bergmann et al.   FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

Cayley-transform-based gradient and conjugate gradient algorithms on Grassmann manifolds

(2021) Xiaojing Zhu et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

Sufficient Descent Riemannian Conjugate Gradient Methods

(2021) Hiroyuki Sakai et al.   JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS

A Riemannian rank-adaptive method for low-rank matrix completion

(2021) Bin Gao et al.   COMPUTATIONAL OPTIMIZATION AND APPLICATIONS

Proximal Gradient Method for Nonsmooth Optimization over the Stiefel Manifold

(2020) Shixiang Chen et al.   SIAM JOURNAL ON OPTIMIZATION

Hybrid Riemannian conjugate gradient methods with global convergence properties

(2020) Hiroyuki Sakai et al.   COMPUTATIONAL OPTIMIZATION AND APPLICATIONS

Riemannian conjugate gradient methods with inverse retraction

(2020) Xiaojing Zhu et al.   COMPUTATIONAL OPTIMIZATION AND APPLICATIONS

Simple Algorithms for Optimization on Riemannian Manifolds with Constraints

(2019) Changshuo Liu et al.   APPLIED MATHEMATICS AND OPTIMIZATION

Primal-dual optimization algorithms over Riemannian manifolds: an iteration complexity analysis

(2019) Junyu Zhang et al.   MATHEMATICAL PROGRAMMING

Iteration-Complexity and Asymptotic Analysis of Steepest Descent Method for Multiobjective Optimization on Riemannian Manifolds

(2019) Orizon P. Ferreira et al.   JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS

Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization of Hadamard Manifolds

(2018) Glaydston de C. Bento et al.   JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS

Cholesky QR-based retraction on the generalized Stiefel manifold

(2018) Hiroyuki Sato et al.   COMPUTATIONAL OPTIMIZATION AND APPLICATIONS

A Riemannian conjugate gradient method for optimization on the Stiefel manifold

(2016) Xiaojing Zhu   COMPUTATIONAL OPTIMIZATION AND APPLICATIONS

A Second Order Nonsmooth Variational Model for Restoring Manifold-Valued Images

(2016) Miroslav Bačák et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

A Dai–Yuan-type Riemannian conjugate gradient method with the weak Wolfe conditions

(2015) Hiroyuki Sato   COMPUTATIONAL OPTIMIZATION AND APPLICATIONS

Low-rank retractions: a survey and new results

(2014) P.-A. Absil et al.   COMPUTATIONAL OPTIMIZATION AND APPLICATIONS

Stochastic Gradient Descent on Riemannian Manifolds

(2013) Silvere Bonnabel   IEEE TRANSACTIONS ON AUTOMATIC CONTROL

A new, globally convergent Riemannian conjugate gradient method

(2013) Hiroyuki Sato et al.   OPTIMIZATION

Projection-like Retractions on Matrix Manifolds

(2012) P.-A. Absil et al.   SIAM JOURNAL ON OPTIMIZATION

Optimization Methods on Riemannian Manifolds and Their Application to Shape Space

(2012) Wolfgang Ring et al.   SIAM JOURNAL ON OPTIMIZATION