Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  considers optimization problems on Riemannian manifolds and analyzes the iteration-complexity for gradient and subgradient methods on manifolds with nonnegative curvatures. By using tools from Riemannian convex analysis and directly exploring the tangent space of the manifold,  obtain different iteration-complexity bounds for the aforementioned methods, thereby complementing and improving related results. Moreover,  also establish an iteration-complexity bound for the proximal point method on Hadamard manifolds.
['G. C. Bento', 'O. P. Ferreira', 'Jefferson G. Melo']
I am writing a research paper on a idea Iteration-complexity of gradient, subgradient and proximal point methods on Riemannian manifolds
[{"from": "human", "value": "I am writing a research paper on a idea Iteration-complexity of gradient, subgradient and proximal point methods on Riemannian manifolds"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  considers optimization problems on Riemannian manifolds and analyzes the iteration-complexity for gradient and subgradient methods on manifolds with nonnegative curvatures. By using tools from Riemannian convex analysis and directly exploring the tangent space of the manifold,  obtain different iteration-complexity bounds for the aforementioned methods, thereby complementing and improving related results. Moreover,  also establish an iteration-complexity bound for the proximal point method on Hadamard manifolds."}]