A Nonmonotone Adaptive-BFGS Trust-Region Method

Abstract

Abstract: A nonmonotone adaptive-BFGS trust-region method for unconstrained optimization is presented.Not only the trust-region radius in this method is automatically determined by using first order information，but combining with the advantage of the BFGS algorithm.Under certain conditions,the global and superlinear convergences of the algorithm are proved.

Key words: unconstrained optimization, nonmonotone algorithm, adaptive trust algorithm, BFGS update, global convergence

JING Shu-Jie, ZHANG Xiao-Liang. A Nonmonotone Adaptive-BFGS Trust-Region Method[J]. journal6, 2009, 30(6): 32-34.

References

[1] SARTENAER A.Automatic Determination of an Initial Trust Region in Nonlinear Pogramming [J].Joumalon on Scientific computing,1997,18(5):1 788-1 803.

[2] ZHANG X S,CHEN Z W,LIAO L Z.A Self-Adaptive Trust Region Method for Unconstrained Optimization [J].Operate Reserch Transactions,2001,5(2):53-62.

[3] ZHANG X S,ZHANG J L,LIAO Z.An Adaptive Trust Region Method and Its Convergence [J].Science in China：Series A,2002,45(4):620-631.

[4] 柯小五，韩继业.无约束最优化的一类非单调信赖域算法 [J].中国科学，1998，28（6）：488-492.

[5] 姚升保.一类带线搜索的非单调信赖域算法 [J].数学杂志,2003，23（3）：290-294.

[6] 李红，焦宝聪.一类带线搜索的非单调自适应信赖域算法 [J].首都师范大学学报:自然科学版,2008，29（2）:1-5.

[7] 李改弟.一个自动确定信赖域半径的信赖域方法 [J].工程数学学报，2006，23（5）：843-848.

[8] 宇振盛，罗成新.带记忆信赖域方法的收敛性分析 [J].运筹与管理，2004，13（2）：16-19.

[9] FU J H,SUN W.Nonmonotone Adaptive Trust-Region Method for Unconstrained Optimization Problems [J].Applied Mathematics and Computation,2005,163(5):489-504.

[10] 陈小军，张超.非线性方程组在几类计算问题中的应用 [J].长沙理工大学学报:自然科学版，2006，3（4）:1-7.

[11] 袁亚湘，孙文瑜.最优化理论与方法 [M].北京：科学出版社，1997.

[12] 袁功林，韦增欣.一个新的BFGS信赖域算法 [J].广西科学，2004，11（3）：195-196.

[13] BACHEM A,GROTSCHEL M,KORTE B.Mathematical Programming:The State of Art [M].Berlin:Springer-Verlag,1983:258-287.

[14] 袁亚湘.信赖域方法的收敛性 [J].计算数学，1994，16（3）：333-346.

[15] BULEAU J P,VIAL J P.Curvilinear Path and Trust Region in Unconstrained Optimization,a Convergence Analysis [J].Math. Prog. Study,1987,30:82-101.

[16] BYRD B H,SCHNABEL R B,SHULTZ G A.Approximate Solution of the Trust Region Problem by Minimization Over Two-Dimensional Subspacea [J].Math. Prog.,1988,40:247-263.