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Global convergence of a modified BFGS-type method for unconstrained non-convex minimization. (English) Zbl 1128.65040
Authors’ summary: To the unconstrained programming of a non-convex function, this article gives a modified Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm associated with the general line search model. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficiency of the new quasi-Newton iteration equation ${B}_{k+1}{s}_{k}={y}_{k}^{*}$, where ${y}_{k}^{*}$ is the sum of ${y}_{k}$ and ${A}_{k}{s}_{k}$, and ${A}_{k}$ is some matrix. The global convergence properties of the algorithm associating with the general form of line search is proved.
##### MSC:
 65K05 Mathematical programming (numerical methods) 90C26 Nonconvex programming, global optimization
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