New Results on Superlinear Convergence of Classical Quasi-Newton Methods
Anton Rodomanov, Yurii Nesterov
Abstract
Abstract We present a new theoretical analysis of local superlinear convergence of classical quasi-Newton methods from the convex Broyden class. As a result, we obtain a significant improvement in the currently known estimates of the convergence rates for these methods. In particular, we show that the corresponding rate of the Broyden–Fletcher–Goldfarb–Shanno method depends only on the product of the dimensionality of the problem and the logarithm of its condition number.
Topics & Concepts
MathematicsRate of convergenceLogarithmApplied mathematicsConvergence (economics)Theory of computationCurse of dimensionalityRegular polygonBroyden–Fletcher–Goldfarb–Shanno algorithmClass (philosophy)Mathematical optimizationMathematical analysisAlgorithmComputer scienceGeometryStatisticsComputer networkAsynchronous communicationEconomicsChannel (broadcasting)Artificial intelligenceEconomic growthAdvanced Optimization Algorithms ResearchIterative Methods for Nonlinear EquationsOptimization and Variational Analysis