A sequential quadratic Hamiltonian algorithm for training explicit RK neural networks

DOI10.1016/j.cam.2021.113943zbMath1480.49004OpenAlexW3217272313WikidataQ114201947 ScholiaQ114201947MaRDI QIDQ2068636

Yanyan Li

Publication date: 20 January 2022

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

Full work available at URL: https://doi.org/10.1016/j.cam.2021.113943

zbMATH Keywords

numerical optimizationmethod of successive approximationsresidual neural networksdiscrete Pontryagin maximum principleRunge-Kutta neural networkssequential quadratic Hamiltonian algorithm

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Learning and adaptive systems in artificial intelligence (68T05) Numerical methods based on necessary conditions (49M05) Neural networks for/in biological studies, artificial life and related topics (92B20) Existence theories for optimal control problems involving ordinary differential equations (49J15) Optimality conditions for problems involving ordinary differential equations (49K15)

Related Items (3)

On the SQH method for solving optimal control problems with non-smooth state cost functionals or constraints ⋮ Accuracy Estimates for Bilinear Optimal Control Problems Governed by Ordinary Differential Equations ⋮ Pointwise error estimates of numerical solutions to linear quadratic optimal control problems

Uses Software

• LBFGS-B
• torchdiffeq

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the proof of Pontryagin's maximum principle by means of needle variations
• Local convergence of an algorithm for solving optimal control problems
• Hedonic housing prices and the demand for clean air
• Runge-Kutta methods in optimal control and the transformed adjoint system
• Symplectic Runge-Kutta discretization of a regularized forward-backward sweep iteration for optimal control problems
• A sequential quadratic Hamiltonian scheme for solving non-smooth quantum control problems with sparsity
• A sequential quadratic Hamiltonian method for solving parabolic optimal control problems with discontinuous cost functionals
• L. S. Pontryagin's maximum principle in the theory of optimal systems. I--III
• An algorithm for the method of successive approximations in optimal control problems
• Method of successive approximations for solution of optimal control problems
• On global convergence of an algorithm for optimal control
• Neural Networks and Deep Learning
• Stable architectures for deep neural networks
• A Limited Memory Algorithm for Bound Constrained Optimization
• Modelling with Ordinary Differential Equations
• On the SQH Scheme to Solve Nonsmooth PDE Optimal Control Problems
• A Maximum Principle of the Pontryagin Type for Systems Described by Nonlinear Difference Equations
• On a method of successive approximations for the solution of problems of optimal control

This page was built for publication: A sequential quadratic Hamiltonian algorithm for training explicit RK neural networks