Formalizes line search methods, conditions, and Zoutendijk theorem in Lean 4 to support verified nonlinear optimization.
A Nonmonotone Line Search Technique for Newton’s Method
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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.
A momentum variant of projected gradient descent is proved to converge with O(epsilon^{-2}) complexity for nonconvex objectives, and is faster than SPG in experiments.
Reinforcement learning learns a policy that adapts control parameters of a regularized interior-point method, accelerating high-accuracy solutions for convex quadratic programs and generalizing across problem classes after lightweight training.
citing papers explorer
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Formalization of Line Search Methods by Lean
Formalizes line search methods, conditions, and Zoutendijk theorem in Lean 4 to support verified nonlinear optimization.
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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.
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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.
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Projected Gradient Methods with Momentum
A momentum variant of projected gradient descent is proved to converge with O(epsilon^{-2}) complexity for nonconvex objectives, and is faster than SPG in experiments.
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Reinforcement learning for adaptive interior point methods in convex quadratic programming
Reinforcement learning learns a policy that adapts control parameters of a regularized interior-point method, accelerating high-accuracy solutions for convex quadratic programs and generalizing across problem classes after lightweight training.