Automatic Optimization |
Common terms and phrases
A₁ Advanced Computing Research Aiping Liao Algorithm automatic differentiation automatic techniques backward recursion bisection method calculate Newton's direction calculate the Newton Coleman and Liao Computing Research Institute control variable convergence Cornell Theory Center D₁ Dependence graph direction of ƒ discrete time optimal discrete-time optimal control DTOC format DTOC problems DTOC setting dummy variable elementary functions Əyi Ti+1 function f ƒDTOC Gaussian elimination gDTOC given by Procedure gradient of ƒ Griewank Hessian H Hessian of ƒ identity matrix In+i intermediate variables j-th component Lemma modified to handle Newton step Ni+1 nonzero element number of operations O(m² objective function optimal control problems Pi+1 PN+1 positive definite Procedure fAD Procedure fDTOC procedure for calculating properties p1)-(p6 Proposition 2.1 relabeled reverse mode applied second order sparse symmetric matrix Ti(Xi Ti(yı total number trust region method vectors Wei Yuan XI is positive y₁ Yi+1 YN+1 Yuying მე ᎥᎢ