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In this paper, we propose a new rank two quasi-Newton method based on adjoint Broyden updates for solving symmetric nonlinear equations, which can be seen as a class of adjoint BFGS method. The new rank two quasi-Newton update not only can guarantee that $B_{k+1}$ approximates Jacobian $F'(x_{k+1})$ along direction $s_k$ exactly, but also shares some nice properties such as positive definiteness and least change property with BFGS method. Under suitable conditions, the proposed method converges globally and superlinearly. Some preliminary numerical results are reported to show that the proposed method is effective and competitive.
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참고문헌 (18)
참고문헌 신청
P. N. Brown / 1994 / Convergence theory of nonlinear Newton-Krylov algorithms / SIAM J. Optim 4(2):297~330
R. H. Byrd / 1989 / A tool for the analysis of quasi-Newton methods with application to unconstrained minimization / SIAM J. Numer. Anal 26(3):727~739
Y. H. Dai / 2002 / Convergence properties of the BFGS algorithm / SIAM J. Optim 13(3):693~701
E. D. Dolan / 2002 / Benchmarking optimization software with performance profiles / Math. Program 91(2):201~213
R. Fletcher / 1991 / A new variational result for quasi-Newton formulae / SIAM J. Optim 1(1):18~21
R. H. Byrd / 1989 / A tool for the analysis of quasi-Newton methods with application to unconstrained minimization / SIAM J. Numer. Anal 26(3):727~739
Y. H. Dai / 2002 / Convergence properties of the BFGS algorithm / SIAM J. Optim 13(3):693~701
E. D. Dolan / 2002 / Benchmarking optimization software with performance profiles / Math. Program 91(2):201~213
R. Fletcher / 1991 / A new variational result for quasi-Newton formulae / SIAM J. Optim 1(1):18~21
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