Calculus Identities for Generalized Simplex Gradients: Rules and Applications

DOI10.1137/18M1215864zbMath1461.90170OpenAlexW2964662941MaRDI QIDQ5853722

Gabriel Jarry-Bolduc, Warren L. Hare

Publication date: 11 March 2021

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/18m1215864

zbMATH Keywords

gradient approximationsimplex gradientcalculus identitiesZitat: 1351.90168

Mathematics Subject Classification ID

Derivative-free methods and methods using generalized derivatives (90C56) Numerical methods for variational inequalities and related problems (65K15)

Related Items (4)

Gradient and diagonal Hessian approximations using quadratic interpolation models and aligned regular bases ⋮ A discussion on variational analysis in derivative-free optimization ⋮ Using orthogonally structured positive bases for constructing positive \(k\)-spanning sets with cosine measure guarantees ⋮ Approximating the diagonal of a Hessian: which sample set of points should be used

Uses Software

• IMFIL
• KELLEY
• minpack

Cites Work

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• The calculus of simplex gradients
• Geometry of interpolation sets in derivative free optimization
• Self-Correcting Geometry in Model-Based Algorithms for Derivative-Free Unconstrained Optimization
• Using Sampling and Simplex Derivatives in Pattern Search Methods
• Geometry of sample sets in derivative-free optimization: polynomial regression and underdetermined interpolation
• Using simplex gradients of nonsmooth functions in direct search methods
• Introduction to Derivative-Free Optimization
• `` Direct Search Solution of Numerical and Statistical Problems
• Testing Unconstrained Optimization Software
• Derivative-Free and Blackbox Optimization
• A Simplex Method for Function Minimization

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