Automatic differentiation of algorithms

DOI10.1016/S0377-0427(00)00422-2zbMath0994.65020WikidataQ56429730 ScholiaQ56429730MaRDI QIDQ1593824

Steven Brown, Michael Bartholomew-Biggs, Bruce Christianson, L. C. W. Dixon

Publication date: 25 January 2001

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

algorithmoptimal controlnumerical examplesinterval analysisnonlinear optimizationerror analysisparallelismautomatic differentiationpenalty functionsprogram transformationfunction approximationcheckpointsimplicit equationsvariable momentumadjoint programming

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Numerical mathematical programming methods (65K05) Nonlinear programming (90C30) Numerical optimization and variational techniques (65K10) General methods in interval analysis (65G40) Parallel numerical computation (65Y05) Numerical differentiation (65D25)

Related Items

An adaptive trust-region method without function evaluations, EAGO.jl: easy advanced global optimization in Julia, On the Halley class of methods for unconstrainedoptimization problems, On the Versatility of Open Logical Relations, Automatic finite element formulation and assembly of hyperelastic higher order structural models, Automation of primal and sensitivity analysis of transient coupled problems, Optimizing preventive maintenance models, Differential logical relations. II: Increments and derivatives, Automatic adjoint differentiation for gradient descent and model calibration, A simple way to improved formulation of \(\text{FE}^2\) analysis, Solution of third grade thin film flow using algorithmic differentiation, Physics-informed deep learning for simultaneous surrogate modeling and PDE-constrained optimization of an airfoil geometry, An artificial neural network as a troubled-cell indicator, Global convergence of a curvilinear search for non-convex optimization, \texttt{tqix.pis}: a toolbox for quantum dynamics simulation of spin ensembles in Dicke basis, Topology optimization based on deep representation learning (DRL) for compliance and stress-constrained design, Approximate supervised learning of quantum gates via ancillary qubits, An improved inexact Newton method, Numerical solution of a third-order nonlinear boundary-value problem by automatic differentiation, Isogeometric structural shape optimization using automatic sensitivity analysis, Automation of finite element formulations for large deformation contact problems, Theoretical efficiency of a new inexact method of tangent hyperbolas, Efficient optimisation of a vehicle suspension system, using a gradient-based approximation method. I: mathematical modelling, Theoretical efficiency of a new inexact method of tangent hyperbolas, Newton step methods for AD of an objective defined using implicit functions, An equation-based algorithmic differentiation technique for differential algebraic equations, Comparing gradient descent with automatic differentiation and particle swarm optimization techniques for estimating tumor blood flow parameters in contrast-enhanced imaging, Bayesian learning via neural Schrödinger-Föllmer flows

Cites Work

• Automatic computation of derivatives with the use of the multilevel differentiating technique. I: Algorithmic basis
• Using forward accumulation for automatic differentiation of implicitly-defined functions
• Geometric approach to Fletcher's ideal penalty function
• Differential dynamic programming and Newton's method
• Recipes for adjoint code construction
• Reverse aumulation and imploicit functions
• Giving reverse differentiation a helping hand^∗
• Cheap Newton steps for optimal control problems: automatic differentiation and Pantoja's algorithm
• A simple automatic derivative evaluation program
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item