| 摘要: |
| 将新的BFGS校正公式Bk+1=Bk+(yk*yk*T)/(skTyk*)-(BkskskTBk)/(skTBksk),与文献[16]中的算法相结合给出一个非单调BFGS校正的信赖域算法.该算法在假设条件:(i)存在常数c1,c2,c3,使得对所有的Δk>0,gk∈Rn,对称正定阵Bk∈Rn×n,有predk ≥ c1||gk||min{Δk,c2||gk||,c3||gk||/||Bk||};(ii)若||Bk-1|| ≤ Δk,则dk=-Bk-1gk;(iii)f(x)是二次连续可微函数,▽2f(xk)是Lipschitz连续,水平集ϕ(x0)有界下,具有全局收敛性和Q-二次收敛性. |
| 关键词: 非单调 BFGS校正 全局收敛性 信赖域算法 |
| DOI： |
| 投稿时间：2006-02-23修订日期：2006-05-24 |
| 基金项目: |
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| A Nonmonotone BFGS-Trust-Region Algorithm |
|
WU Qing-jun
|
| (Department of Mathematics and Computer Science, Yulin Teachers's College, Yulin, Guangxi, 537000, China) |
| Abstract: |
| A new nonmonotone BFGS-trust-region algorithm is proposed by combining the BFGS update Bk+1=Bk+ (yk*yk*T)/ (skTyk*)- (BkskskTBk)/ (skTBksk), with the algorithm given in references[16].The global and Q-quadratic convergences of the proposed algorithm are also proved under the following conditions: (i)there are constants c1, c2, c3 such that predk ≥ c1‖gk‖ min{Δk, c2‖gk‖, c3‖gk‖/‖Bk‖}for Δk>0, gk∈Rn and some symmetry positive definite matrix Bk∈Rn×n; (ii)dk=-Bk-1gk if ‖Bk-1gk‖ ≤ Δk and (iii) f (x) is a second-order continuously differentiable function, ▽2f (x) is Lipschitz continuous and the level set ϕ (x0) is bounded. |
| Key words: nonmonotone BFGS update global convergence trustregion algorithm |
