A Riemannian Dennis-Moré Condition

Gallivan, Kyle A.; Qi, Chunhong; Absil, Pierre-Antoine

doi:10.1007/978-1-4471-2437-5_14

Cited by 5 publications

(3 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proof. Note that the Riemannian Newton iteration in (14) for the modified complementarity condition yields…”

Section: Prototype Algorithmmentioning

confidence: 99%

“…This condition encompasses a large category of well-known update formulas, such as BFGS. Gallivan et al [14] have generalized it to the Riemannian quasi-Newton methods. In this section, we give an analogous Dennis Moré condition for our quasi-Newton RIP by Theorem 6.1, and establish its superlinear convergence by Theorem 6.2.…”

Section: Local and Superlinear Convergence Of Quasi-newton Ripmentioning

confidence: 99%

See 1 more Smart Citation

Riemannian Interior Point Methods for Constrained Optimization on Manifolds

Lai¹,

Yoshise²

2022

Preprint

View full text Add to dashboard Cite

We extend the classical primal-dual interior point algorithms from Euclidean setting to Riemannian setting. This is named as Riemannian Interior Point (RIP) Method for the Riemannian constrained optimization problem. Under the standard assumptions in Riemannian setting, we establish the locally superlinear, quadratic convergence for Newton version of RIP, and the locally linear, superlinear convergence for quasi-Newton version of RIP. Those are the generalizations of classical local convergence theory of primal-dual interior point algorithms for nonlinear programming, proposed by El-Bakry et al. in 1996, andYamashita et al. in 1996.

show abstract

“…Proof. Note that the Riemannian Newton iteration in (14) for the modified complementarity condition yields…”

Section: Prototype Algorithmmentioning

confidence: 99%

Section: Local and Superlinear Convergence Of Quasi-newton Ripmentioning

confidence: 99%

Riemannian Interior Point Methods for Constrained Optimization on Manifolds

Lai¹,

Yoshise²

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…-Note that the condition in corollary 3.3 is similar to the Dennis-Moré condition [10,8], which is also applicable for quasi-Newton update techniques on Riemannian manifolds [28,17]. The application of the exponential mapping within the Newton method is an expensive operation.…”

Section: Convergence Of Riemannian Newtonmentioning

confidence: 99%