函数空间中总极值的R收敛有限维逼近

陈熙; 姚奕荣; 郑权

doi:10.3879/j.issn.1000-0887.2011.01.011

函数空间中总极值的R收敛有限维逼近

doi: 10.3879/j.issn.1000-0887.2011.01.011

陈熙¹,
姚奕荣¹,
郑权^1,2

上海大学理学院数学系,上海200444;2.哥伦布州立大学数学系,乔治州哥伦布市31907,美国

基金项目: 国家自然科学基金资助项目(10771158);上海市重点学科资助项目(S30104)

详细信息

作者简介:
陈熙(1986- ),男,硕士生(E-mail:chenxi@shu.edu.cn);姚奕荣(联系人.E-mail:yryao@staff.shu.edu.cn).

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出版历程
- 收稿日期: 2010-09-20
- 修回日期: 2010-11-24
- 刊出日期: 2011-01-15

Finite Dimensional Approximation to Global Minimizers in Functional Spaces With R-Convergence

Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;

摘要

摘要: 应用测度序列R-收敛的新概念来描述函数空间中总极值问题解的有限维逼近，并利用变差积分途径来寻找这样的解．针对有约束问题，运用罚变差积分算法把所给问题转化为无约束问题，且给出一个非凸状态约束最优控制问题的数值例子以说明该算法的有效性．
- 总极值 /
- 变差积分 /
- 变测度 /
- R-收敛 /
- 有限维逼近
Abstract: New concept of convergence(R-convergence)of a sequence of measures was applied to characterize global minimizers in functional space as a sequence of approximating solutions in finite-dimensional spaces.A deviation integral approach was used to find such solutions.For a constrained problem,a penalized deviation integral algorithm was proposed to convert it to unconstrained ones.A numerical example on optimal control problem with non convex state constrains was given to show that the algorithm is efficient.
- global optimization /
- deviation integral /
- variable measure /
- R-convergence /
- finite dimensional approximation

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参考文献(12)

[1]	Zheng Q, Zhuang D. Integral global optimization of constrained problems in functional spaces with discontinuous penalty functions[C]Floundas C A, Pardalos P M.Recent Advances in Global Optimization. New Jersey: Princeton University Press, 1992, 298-320.
[2]	HE Zhen-zhen, CUI Hong-quan, ZHENG Quan. Finite dimensional approximation to global minima—an integral approach[J]. OR Transactions, 2005, 9(1): 21-31.
[3]	Phu H X, Hoffmann A. Essential supremum and supremum of summable functions[J]. Numer Funct Anal and Optimiz, 1996, 17(1/2): 167-180.
[4]	WU Dog-hua, YU Wu-yang, ZHENG Quan. A sufficient and necessary condition for global optimization[J]. Applied Mathematics Letters, 2010, 23(1): 17-21. doi: 10.1016/j.aml.2009.07.020
[5]	陈柳，姚奕荣，郑权. 变差积分型约束总极值问题的不连续罚函数[J]. 应用数学和力学, 2009, 30(9)：1125-1134.(CHEN Liu, YAO Yi-rong, ZHENG Quan. Discontinuous penalty approach with deviation integral for global constrained minimization[J]. Applied Mathematics and Mechanics(English Edition),2009, 30(9)：1201-1210.)
[6]	YAO Yi-rong,CHEN Liu, ZHENG Quan. Optimality condition and algorithm with deviation integral for global optimaization[J]. Journal of Mathematical Analysis and Applications,2009, 357(2): 371-384. doi: 10.1016/j.jmaa.2009.04.022
[7]	SHI Shu-zhong, ZHENG Quan, ZHUANG De-ming. Discontinuous robust mapping are approximatable[J]. Trans Amer Math Soc, 1995, 347(12): 4943-4957. doi: 10.1090/S0002-9947-1995-1308024-X
[8]	ZHENG Quan. Robust analysis and global minimization of a class of discontinuous functions (I)[J]. Acta Mathematicae Applicatae Sinica, English Ser, 1990, 6(3): 205-223. doi: 10.1007/BF02019147
[9]	ZHENG Quan. Robust analysis and global minimization of a class of discontinuous functions (II)[J]. Acta Mathematicae Applicatae Sinica, English Ser, 1990, 6(3): 317-337. doi: 10.1007/BF02015339
[10]	ZHENG Quan. Robust analysis and global optimization[J]. International J Computers and Mathematics With Applications, 1990, 24(1): 273-286.
[11]	HONG Chew Soo, ZHENG Quan. Integral Global Optimization-Theory, Implementation and Applications[M]. Berlin Heidelberg: Spring-Verlag, 1988.
[12]	ZHENG Quan, Zhang L. Global minimization of constrained problems with discontinuous penalty functions[J]. International J Computers and Mathematics With Applications, 1999, 37(4/5): 41-58.

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函数空间中总极值的R收敛有限维逼近

doi: 10.3879/j.issn.1000-0887.2011.01.011

作者简介:
陈熙(1986- ),男,硕士生(E-mail:chenxi@shu.edu.cn);姚奕荣(联系人.E-mail:yryao@staff.shu.edu.cn).

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Finite Dimensional Approximation to Global Minimizers in Functional Spaces With R-Convergence

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函数空间中总极值的R收敛有限维逼近

doi: 10.3879/j.issn.1000-0887.2011.01.011

作者简介: 陈熙(1986- ),男,硕士生(E-mail:chenxi@shu.edu.cn);姚奕荣(联系人.E-mail:yryao@staff.shu.edu.cn).

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出版历程

Finite Dimensional Approximation to Global Minimizers in Functional Spaces With R-Convergence

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出版历程

目录

作者简介:
陈熙(1986- ),男,硕士生(E-mail:chenxi@shu.edu.cn);姚奕荣(联系人.E-mail:yryao@staff.shu.edu.cn).