Formalizes line search methods, conditions, and Zoutendijk theorem in Lean 4 to support verified nonlinear optimization.
A Nonmonotone Line Search Technique and Its Application to Unconstrained Optimization
4 Pith papers cite this work, alongside 620 external citations. Polarity classification is still indexing.
4
Pith papers citing it
620
external citations · OpenAlex
citation-role summary
background 1
citation-polarity summary
fields
math.OC 4roles
background 1polarities
background 1representative citing papers
A variable-metric non-monotone line search method based on the Fukushima regularized gap function is introduced for mixed variational inequalities and equilibrium problems, with global convergence and R-linear rate proved under strong monotonicity.
A proximal limited-memory quasi-Newton scheme is developed for nonsmooth nonconvex optimization, with global convergence proven under mild assumptions and rates under the Kurdyka-Lojasiewicz property.
citing papers explorer
-
Formalization of Line Search Methods by Lean
Formalizes line search methods, conditions, and Zoutendijk theorem in Lean 4 to support verified nonlinear optimization.
-
A Variable-Metric Non-monotone Line Search Method for Mixed Variational Inequalities and Equilibrium Problems
A variable-metric non-monotone line search method based on the Fukushima regularized gap function is introduced for mixed variational inequalities and equilibrium problems, with global convergence and R-linear rate proved under strong monotonicity.
-
Proximal Limited-Memory Quasi-Newton Methods for Nonsmooth Nonconvex Optimization
A proximal limited-memory quasi-Newton scheme is developed for nonsmooth nonconvex optimization, with global convergence proven under mild assumptions and rates under the Kurdyka-Lojasiewicz property.
- A Riemannian gradient descent method for optimization on the indefinite Stiefel manifold