What does this research mean for the field?

Gradient-type methods with non-monotone line search on Riemannian manifolds achieve asymptotic convergence and iteration-complexity bounds comparable to traditional Euclidean gradient-type methods. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To analyze the asymptotic convergence and iteration-complexity bounds of gradient-type optimization methods using generalized non-monotone line search strategies on Riemannian manifolds.

September 5, 2026Journal of Scientific ComputingOpen Access

Iteration of Complexity and Asymptotic Analysis of Gradient-Type Methods with Non-monotone Line Search on Riemannian Manifolds

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Authors

QAQamrul Hasan AnsariKing Fahd University of Petroleum and Minerals OFO. P. FerreiraUniversidade Federal de Goiás MUMoin UddinKing Fahd University of Petroleum and Minerals

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Implication

Algorithmic analysis demonstrates Euclidean-level convergence rates and iteration complexity for non-monotone gradient methods on Riemannian manifolds, suggesting improved per-iteration efficiency.

Key Points

To analyze the asymptotic convergence and iteration-complexity bounds of gradient-type optimization methods using generalized non-monotone line search strategies on Riemannian manifolds.
Formulated a Riemannian optimization framework utilizing gradient search directions combined with a generalized non-monotone line search scheme for iterative stepsize selection.
Conducted asymptotic convergence and iteration-complexity analyses alongside numerical experiments to evaluate practical performance.
Proved that gradient-type methods with non-monotone line search on Riemannian manifolds match the iteration-complexity bounds and asymptotic convergence properties of classical Euclidean methods.
Showed through numerical experiments that the framework enables flexible line search options that effectively reduce the computational cost per iteration.

Cite This Study

Ansari et al. (2026) studied this question.

synapsesocial.com/papers/6a9bd3f16b95aff0620eb394 https://doi.org/10.1007/s10915-026-03456-9

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Implication

Algorithmic analysis demonstrates Euclidean-level convergence rates and iteration complexity for non-monotone gradient methods on Riemannian manifolds, suggesting improved per-iteration efficiency.

Iteration of Complexity and Asymptotic Analysis of Gradient-Type Methods with Non-monotone Line Search on Riemannian Manifolds

Discussion

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Implication

Key Points

Cite This Study

Iteration of Complexity and Asymptotic Analysis of Gradient-Type Methods with Non-monotone Line Search on Riemannian Manifolds

Discussion

Member takes

Implication

Key Points

Cite This Study

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