一类二阶逼近集合和二阶逼近导数

华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (5): 49-59.

一类二阶逼近集合和二阶逼近导数

廖春美, 李明华

重庆大学数学与统计学院, 重庆 401331

收稿日期:2010-09-01 修回日期:2010-12-01 出版日期:2011-09-25 发布日期:2011-11-22

A Class of second-order approximating sets and derivatives

LIAO Chun-mei, LI Ming-hua

College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

Received:2010-09-01 Revised:2010-12-01 Online:2011-09-25 Published:2011-11-22

摘要/Abstract

摘要： 首先引入了一类二阶逼近集合和二阶逼近导数. 然后讨论了这些二阶逼近集合之间的关系. 最后利用一种叫做二阶逼近Φ相依集合, 研究了一类集值映射的二阶可微性.

关键词: 二阶逼近导数, 二阶逼近集合, 可微性质

Abstract: A class of second-order approximating sets and second-order derivatives were introduced. The relationships among second-order approximating sets were discussed. Finally, by using so-called second-order approximating Φ-contingent set, second-order differential properties of a class of set-valued maps were investigated.

Key words: second-order approximating derivatives, second-order approximating sets, differential properties

中图分类号:

O224

廖春美, 李明华. 一类二阶逼近集合和二阶逼近导数[J]. 华东师范大学学报(自然科学版), 2011, 2011(5): 49-59.

LIAO Chun-mei, LI Ming-hua. A Class of second-order approximating sets and derivatives[J]. Journal of East China Normal University(Natural Sc, 2011, 2011(5): 49-59.

参考文献

{1} AUBIN J P, FRANKOWSKA H. Set-Valued Analysis [M]. Boston: Birkh\"{a}user, 1990.
{2} AUBIN J P, EKELAND I. Applied Nonlinear Analysis [M]. New York: John Wiley and Sons, 1984.
{3} JAHJ J, KHAN A A, ZEILINGER P. Second-order optimality conditions in set optimization [J]. Journal of Optimization Theory and Applications, 2005, 125: 331-347.
{4} KALASHNIKOV V, JADAMBA B, KHAN A A. First and second-order optimality conditions in set optimization [M]//

Optimization with Multivalued Mappings. New York: Springer, 2006 (2): 265-276.
{5} LI S J , TEO K L, YANG X Q. Higher-order optimaltiy conditons for set-valued optimization [J]. Journal of Optimization Theory and Applications, 2008, 137: 533-553.
{6} LI S J, CHEN C R. Higher order optimality condtions for Henig efficient solutions in set-valued optimization [J]. Journal of Mathematical Analysis and Applications, 2006, 323: 1184-1200.
{7} KHANH P Q, TUAN N D. Higher-order variational sets and higher-order optimality conditions for proper efficiency in set-valued nonsmooth vector optimization [J]. Journal of Optimization Theory and Applications, 2008, 139: 243-261.
{8} TANINO T. Sensitivity analysis in multiobjective optimization [J]. Journal of Optimization Theory and Applications, 1988, 56: 479-499.
{9} SHI D S. Contingent derivative of the perturbation map in multiobjective optimization [J]. Journal of Optimization Theory and Applications, 1991, 70: 385-396.
{10} SHI D S. Sensitivity analysis in convex vector optimization [J]. Journal of Optimization Theory and Applications, 1993, 77: 145-159.
{11} LI S J, YAN H, CHEN G Y. Differential and sensitivity properties of gap functions for vector variational inequalities [J]. Mathematical Methods of Operations Research, 2003, 57: 377-391.
{12} MENG K W, LI S J. Differential and sensitivity properties of gap functions for Minty vector variational inequalities [J]. Journal of Mathematical Analysis and Applications, 2008, 337: 386-398.
{13} LI M H, LI S J. Second-order differential and sensitivity properties of weak vector variational inequalities [J]. Journal of Optimization Theory and Applications, 2010, 144: 76-87.
{14} BONNANS J F, SHAPIRO A. Perturbation Analysis of Optimization Problems [M]. New York: Springer-Verlag, 2000.

{15} ROCKAFELLLAR R T, WETS R J B. Variational Analysis [M]. Berlin: Springer, 1998.

[1]	陈杰, 孙霄龙, 莫玮. 空间绳牵引并联机器人多目标优化设计[J]. 华东师范大学学报(自然科学版), 2015, 2015(1): 142-150.
[2]	杨若愚. 几类向量值极大极小不等式[J]. 华东师范大学学报(自然科学版), 2013, 2013(2): 116-123.
[3]	方志苗, 张宇, 陈桃. 参数字典序向量平衡问题的下半连续性[J]. 华东师范大学学报(自然科学版), 2013, 2013(2): 131-135, 145.
[4]	方志苗, 王丽娜. 广义向量平衡问题的Holder连续性[J]. 华东师范大学学报(自然科学版), 2011, 2011(5): 33-41.