The Structure of Conservative Gradient Fields

DOI10.1137/21M1393637zbMath1471.49013arXiv2101.00699OpenAlexW3195613836MaRDI QIDQ5010051

Tonghua Tian, Adrian S. Lewis

Publication date: 24 August 2021

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

Full work available at URL: https://arxiv.org/abs/2101.00699

zbMATH Keywords

stratificationautomatic differentiationClarke subdifferentialvariational analysisdeep learningsemialgebraicconservative fieldsubgradient descent

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Derivative-free methods and methods using generalized derivatives (90C56) Numerical optimization and variational techniques (65K10) Variational inequalities (49J40) Nonsmooth analysis (49J52) Semialgebraic sets and related spaces (14P10)

Related Items (2)

Conservative and semismooth derivatives are equivalent for semialgebraic maps ⋮ Conservative parametric optimality and the ridge method for tame min-max problems

Uses Software

• TensorFlow
• PyTorch

Cites Work

• Unnamed Item
• On Lipschitz optimization based on gray-box piecewise linearization
• Geometric categories and o-minimal structures
• Conservative set valued fields, automatic differentiation, stochastic gradient methods and deep learning
• Stochastic subgradient method converges on tame functions
• Clarke Subgradients of Stratifiable Functions
• Evaluating Derivatives
• Optimization and nonsmooth analysis

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