Kantorovich's theorem on Newton's method in Riemannian manifolds
From MaRDI portal
Publication:1599205
DOI10.1006/jcom.2001.0582zbMath1003.65057OpenAlexW2066214692WikidataQ115395639 ScholiaQ115395639MaRDI QIDQ1599205
Benar Fux Svaiter, Orizon P. Ferreira
Publication date: 8 January 2003
Published in: Journal of Complexity (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jcom.2001.0582
Singularities of vector fields, topological aspects (58K45) Numerical solutions to equations with nonlinear operators (65J15)
Related Items
Riemannian optimization and multidisciplinary design optimization, Newton algorithm on constraint manifolds and the 5-electron Thomson problem, Computing the Conformal Barycenter, Proximal point methods for Lipschitz functions on Hadamard manifolds: scalar and vectorial cases, On maximal monotonicity of bifunctions on Hadamard manifolds, Kantorovich's majorants principle for Newton's method, Local convergence analysis of inexact Newton method with relative residual error tolerance under majorant condition in Riemannian manifolds, Symplectic methods for the approximation of the exponential map and the Newton iteration on Riemannian submanifolds, Kantorovich's theorem for Newton's method on Lie groups, Robust semi-local convergence analysis for inexact Newton method, Newton-type methods on Riemannian manifolds under Kantorovich-type conditions, Local convergence of the Newton’s method in two step nilpotent Lie groups, Kantorovich's theorem on Newton's method under majorant condition in Riemannian manifolds, An efficient damped Newton-type algorithm with globalization strategy on Riemannian manifolds, Newton method for finding a singularity of a special class of locally Lipschitz continuous vector fields on Riemannian manifolds, A subgradient method for multiobjective optimization on Riemannian manifolds, On the superlinear convergence of Newton's method on Riemannian manifolds, Damped Newton's method on Riemannian manifolds, Monotone and accretive vector fields on Riemannian manifolds, An accelerated first-order method for non-convex optimization on manifolds, Convergence criteria of Newton's method on Lie groups, A Riemannian view on shape optimization, Non‐linear space‐time elasticity, CONJECTURES ABOUT SIMPLE DYNAMICS FOR SOME REAL NEWTON MAPS ON ℝ2, Faster Riemannian Newton-type optimization by subsampling and cubic regularization, Chebyshev-Halley's method on Riemannian manifolds, Convergence of Newton's method for sections on Riemannian manifolds, A robust Kantorovich's theorem on the inexact Newton method with relative residual error tolerance, Convergence of the Gauss-Newton method for convex composite optimization problems under majorant condition on Riemannian manifolds, Gauss-Newton method for convex composite optimizations on Riemannian manifolds, On a bilinear operator free third order method on Riemannian manifolds, Convergence rate of descent method with new inexact line-search on Riemannian manifolds, Newton's method for sections on Riemannian manifolds: Generalized covariant \(\alpha \)-theory, A robust semi-local convergence analysis of Newton's method for cone inclusion problems in Banach spaces under affine invariant majorant condition, Stochastic Approximation for Optimization in Shape Spaces, Traub-type high order iterative procedures on Riemannian manifolds, Expanding the applicability of the Gauss-Newton method for convex optimization under a majorant condition, Modified Tseng's extragradient methods for variational inequality on Hadamard manifolds, An improved unifying convergence analysis of Newton's method in Riemannian manifolds, Third-order methods on Riemannian manifolds under Kantorovich conditions, On topological index of solutions for variational inequalities on Riemannian manifolds, ON THE SEMILOCAL CONVERGENCE OF NEWTON'S METHOD FOR SECTIONS ON RIEMANNIAN MANIFOLDS, Unconstrained steepest descent method for multicriteria optimization on Riemannian manifolds, Newton’s method for variational inequality problems: Smale’s point estimate theory under the γ-condition, The Kantorovich theorem and interior point methods, Local convergence of Newton's method on Lie groups and uniqueness balls, Convergence analysis of inexact proximal point algorithms on Hadamard manifolds, Unnamed Item, Uniqueness of the singular points of vector fields on Riemannian manifolds under the \(\gamma\)-condition, Extending the applicability of Newton's method on Lie groups, Existence of solutions for variational inequalities on Riemannian manifolds, Local convergence of Newton's method on the Heisenberg group, A framework for generalising the Newton method and other iterative methods from Euclidean space to manifolds, Adaptive regularization with cubics on manifolds, On transversal connecting orbits of Lagrangian systems in a nonstationary force field: the Newton-Kantorovich approach, Generalized weak sharp minima in cone-constrained convex optimization on Hadamard manifolds, A global Newton method for the nonsmooth vector fields on Riemannian manifolds, Modified proximal point algorithms on Hadamard manifolds, Smale's point estimate theory for Newton's method on Lie groups, Gap functions and globally projected differential inclusions on Riemannian manifolds, Proximal point method for a special class of nonconvex functions on Hadamard manifolds, Concerning the convergence of Newton's method and quadratic majorants, Newton's method for approximating zeros of vector fields on Riemannian manifolds, Extended Newton Methods for Multiobjective Optimization: Majorizing Function Technique and Convergence Analysis, Newton's method on Lie groups, Finite termination of the proximal point method for convex functions on Hadamard manifolds, Proximal Point Algorithms on Hadamard Manifolds: Linear Convergence and Finite Termination, EXTENDING THE APPLICABILITY OF NEWTON'S METHOD ON RIEMANNIAN MANIFOLDS WITH VALUES IN A CONE, Unnamed Item, A short survey on Kantorovich
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- The imbedding problem for Riemannian manifolds
- A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions
- Minimizing a differentiable function over a differential manifold
- A unified approach for constructing fast two-step Newton-like methods
- Shadowing orbits and Kantorovich's theorem
- A NEW TECHNIQUE FOR THE CONSTRUCTION OF SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS
- Complexity of Bezout's Theorem I: Geometric Aspects
- The Geometry of Algorithms with Orthogonality Constraints
- Optimization Techniques on Riemannian Manifolds
- New results on newton-kantorovich approximations with applications to nonlinear integral equations
- The Newton-Kantorovich Theorem
- On the Kantorovich Hypothesis for Newton’s Method
