Riemannian Interior Point Methods for Constrained Optimization on Manifolds

DOI10.1007/S10957-024-02403-8MaRDI QIDQ6493979

Zhijian Lai, Akiko Yoshise

Publication date: 29 April 2024

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Programming in abstract spaces (90C48)

Cites Work

• Computational experience with a primal-dual interior point method for linear programming
• Superlinear and quadratic convergence of some primal - dual interior point methods for constrained optimization
• Global convergence of the Newton interior-point method for nonlinear programming
• Kantorovich's theorem on Newton's method in Riemannian manifolds
• On the formulation and theory of the Newton interior-point method for nonlinear programming
• On the Newton interior-point method for nonlinear programming problems
• Nonnegative low rank matrix approximation for nonnegative matrices
• Simple algorithms for optimization on Riemannian manifolds with constraints
• Riemannian conjugate gradient methods with inverse retraction
• Sequential optimality conditions for nonlinear optimization on Riemannian manifolds and a globally convergent augmented Lagrangian method
• Damped Newton's method on Riemannian manifolds
• A brief introduction to manifold optimization
• A Riemannian symmetric rank-one trust-region method
• On the superlinear convergence of Newton's method on Riemannian manifolds
• An Introduction to Optimization on Smooth Manifolds
• Sequential Quadratic Optimization for Nonlinear Optimization Problems on Riemannian Manifolds
• An SQP Method for Equality Constrained Optimization on Hilbert Manifolds
• Intrinsic Formulation of KKT Conditions and Constraint Qualifications on Smooth Manifolds

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