| The Global Convergence of Self-Scaling BFGS Algorithm with Nonmonotone Line Search for Unconstrained Nonconvex Optimization Problems |
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| 作者姓名： | Hong Xia YIN Dong Lei DU |
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| 作者单位： | [1]Chinese Academy of Sciences Research Center on Data Technology and Knowledge Economy, Department of Mathematics, Graduate University of the Chinese Academy of Sciences, Beijing 100049, P. R. China [2]Faculty of Administration, University of New Brunswick, P.O. Box 4400, Fredericton, NB E3B 5A3, New Brunswick, Canada |
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| 基金项目： | The first author is supported by NSFC 10001031 and 70472074; The second author is supported in part by NSERC Grant 283103; |
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| 摘 要： | The self-scaling quasi-Newton method solves an unconstrained optimization problem by scaling the Hessian approximation matrix before it is updated at each iteration to avoid the possible large eigenvalues in the Hessian approximation matrices of the objective function. It has been proved in the literature that this method has the global and superlinear convergence when the objective function is convex （or even uniformly convex）. We propose to solve unconstrained nonconvex optimization problems by a self-scaling BFGS algorithm with nonmonotone linear search. Nonmonotone line search has been recognized in numerical practices as a competitive approach for solving large-scale nonlinear problems. We consider two different nonmonotone line search forms and study the global convergence of these nonmonotone self-scale BFGS algorithms. We prove that, under some weaker condition than that in the literature, both forms of the self-scaling BFGS algorithm are globally convergent for unconstrained nonconvex optimization problems.
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| 关 键 词： | 非单调线搜索 全局收敛性 无约束最优化 BFGS算法 |
| 收稿时间： | 7 December 2004 |
| 修稿时间： | 2004-12-072005-04-18 |
The Global Convergence of Self-Scaling BFGS Algorithm
with Nonmonotone Line Search for
Unconstrained Nonconvex Optimization Problems |
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| Hong Xia YIN Dong Lei DU.The Global Convergence of Self-Scaling BFGS Algorithm with Nonmonotone Line Search for Unconstrained Nonconvex Optimization Problems[J].Acta Mathematica Sinica,2007,23(7):1233-1240. |
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| Authors: | Hong Xia Yin Dong Lei Du |
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| Institution: | (1) Chinese Academy of Sciences Research Center on Data Technology and Knowledge Economy, Department of Mathematics, Graduate University of the Chinese Academy of Sciences, Beijing 100049, P. R. China;(2) Faculty of Administration, University of New Brunswick, 4400, Fredericton, NB E3B 5A3, New Brunswick, Canada |
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| Abstract: | The self-scaling quasi-Newton method solves an unconstrained optimization problem by
scaling the Hessian approximation matrix before it is updated at each iteration to avoid the possible
large eigenvalues in the Hessian approximation matrices of the objective function. It has been proved
in the literature that this method has the global and superlinear convergence when the objective function
is convex (or even uniformly convex). We propose to solve unconstrained nonconvex optimization
problems by a self-scaling BFGS algorithm with nonmonotone linear search. Nonmonotone line search
has been recognized in numerical practices as a competitive approach for solving large-scale nonlinear
problems. We consider two different nonmonotone line search forms and study the global convergence
of these nonmonotone self-scale BFGS algorithms. We prove that, under some weaker condition
than that in the literature, both forms of the self-scaling BFGS algorithm are globally convergent for
unconstrained nonconvex optimization problems.
The first author is supported by NSFC 10001031 and 70472074
The second author is supported in part by NSERC Grant 283103 |
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| Keywords: | nonmonotone line search self-scaling BFGS method global convergence |
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