\(\rho\)-regularization subproblems: strong duality and an eigensolver-based algorithm

DOI10.1007/s10589-021-00341-zzbMath1487.90609arXiv2109.01829OpenAlexW3198203964MaRDI QIDQ2114814

Ting Kei Pong, Liaoyuan Zeng

Publication date: 15 March 2022

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

Full work available at URL: https://arxiv.org/abs/2109.01829

zbMATH Keywords

eigensolver-based algorithmRendl-Wolkowicz dual problemtrust-region type method

Mathematics Subject Classification ID

Nonlinear programming (90C30) Optimality conditions and duality in mathematical programming (90C46)

Uses Software

• LSTRS
• GQTPAR
• HSL-VF05

Cites Work

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• The generalized trust region subproblem
• Adaptive cubic regularisation methods for unconstrained optimization. I: Motivation, convergence and numerical results
• On solving trust-region and other regularised subproblems in optimization
• A semidefinite framework for trust region subproblems with applications to large scale minimization
• Convex analysis and nonlinear optimization. Theory and examples
• Cubic regularization of Newton method and its global performance
• A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem
• Minimizing a Quadratic Over a Sphere
• Solving the Trust-Region Subproblem By a Generalized Eigenvalue Problem
• Computing a Trust Region Step
• Algorithm 873
• Trust Region Methods
• Theory and application of p-regularized subproblems for p>2
• The trust region subproblem and semidefinite programming*
• Solving the Trust-Region Subproblem using the Lanczos Method
• Indefinite Trust Region Subproblems and Nonsymmetric Eigenvalue Perturbations
• Solving Large-Scale Cubic Regularization by a Generalized Eigenvalue Problem
• Error estimates for iterative algorithms for minimizing regularized quadratic subproblems
• Convex Analysis