A Modified BFGS Method |
Common terms and phrases
9j+M 9k+M analysis of quasi-Newton B₁ B₂ BFGS METHOD Ai-Ping BFGS method corrects BFGS method performs Bk+1 BkSk Bo-In Bo+ln BRSK Busk Byrd and Nocedal circumstances this modified CORNELL UNIVERSITY corrects large eigenvalues corrects the eigenvalues cos2 Cos² Øk denotes det(B due to Byrd e-Bo eigenvalues better eigenvalues more efficiently equality holds f satisfies Assumption FORTRAN function evaluations global convergence gradient of ƒ inequality of 25 inexact line search largest real root least pk Lemma Liao line search satisfying matrix modified BFGS method modified BFGS update Nocedal and Yuan Note that cos20 number of function numbers of iterations Numerical results obtain the condition positive definite presents the numbers quasi-Newton equation quasi-Newton methods rank-one update self-correcting property sign of equality Sk det(Bk+1 sk)² ST Bk Sk styk Suppose that f term in 11 Theorem 2.5 tr(Bk tr(Bk+1 Wolfe condition y‡sk ysk)² µmk