Abstract
To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the quasi-Newton iteration pattern. We prove the global convergence properties of the algorithm associating with the general form of line search, and prove the quadratic convergence rate of the algorithm under some conditions.
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Jian-Guo Liu is a doctoral student in Institute of System Engineering, Dalian University of Technology. His research interests are the numerical computation and software, numerical methods for optimization, System Engineering.
Qiang Guo is doctor in Department of Applied Mathematics and Physics, Dalian National University. Her research interests are the optimal design, numerical computation and software, numerical methods for optimization, optimization methods in science and engineering, nonsmooth optimization.
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Liu, JG., Guo, Q. Global convergence properties of the modified BFGS method associating with general line search model. JAMC 16, 195–205 (2004). https://doi.org/10.1007/BF02936161
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DOI: https://doi.org/10.1007/BF02936161