Abstract
The Broyden-type algorithm is one of the most effective quasi-Newton methods for solving unconstrained optimization problems. However, the study of the global convergence of the Broyden-type algorithm is not enough. Motivated by Andrei (J. Comput. Appl. Math. 332: 26–44, 2018), we present a modified two-parameter scaled Broyden-type algorithm. Some approaches are used in the designed method: (1) we introduce a modified Broyden-type formula with two parameters; (2) we use approximated parameter settings to reduce the effect of eigenvalues of sequence {Bk}; (3) we propose a modified weak Wolfe–Powell line search technique with projection technique to avoid using failed search direction. The parameters of our study have the same functionality, that of correcting the structure of the eigenvalues of the approximate Hessian matrix. The difference is in the approach of 4-term Broyden updates instead of BFGS. Numerical performance shows that the modified Broyden-type algorithm is competitive with the classical Broyden approach.
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