[1]赵亮,刘学文.Stampacchia型和Minty型似变分不等式解的性质[J].江西师范大学学报(自然科学版),2012,(06):598-601.
　CAO Han-wen,TIAN Wei.The Properties of the Solution in Stampacchia-Type and Minty-Type Variational-Like Inequalities[J].Journal of Jiangxi Normal University:Natural Science Edition,2012,(06):598-601.
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Stampacchia型和Minty型似变分不等式解的性质()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2012年06期
页码:
598-601
栏目:
出版日期:
2012-12-01

文章信息/Info

Title:
The Properties of the Solution in Stampacchia-Type and Minty-Type Variational-Like Inequalities
作者:
赵亮;刘学文
重庆师范大学数学学院, 重庆 401331
Author(s):
CAO Han-wen;  TIAN Wei
关键词:
解集; 伪单调; 间隙函数; 似变分不等式
Keywords:
solution set; pseudomonotone; gap function; variational-like inequalities
分类号:
O110.74
文献标志码:
A
摘要:
在实n维欧式空间Rn中利用上Dini方向导数构造了Minty型似变分不等式的间隙函数()G x ,并在此基础上讨论了Stampacchia型和Minty型这两类似变分不等式的解与()G x 的关系,得到了2类似变分不等式解集相等的1个充分条件.
Abstract:
Gap function G(x) of the Minty-type variational-like inequalities was constructed by upper Dini direc-tional derivative in a real n-dimensional Euclidean space. And some relations between solutions of Stampac-chia-type and Minty-type variational-like inequalities and G(x) are investigated. A sufficient condition of two class of variational-like inequality solution sets equal is obtained.

参考文献/References:

[1] Parida J, Sahoo M, Kumar A. A variational-like inequality problem [J]. Bulletin of the Australian Mathematical Society, 1989, 39(2): 225-231.
[2] Crespi G P, Ginchev I, Rocca M. Minty variational inequalities, increase along rays property and optimization [J]. Journal of Optimization Theory and Applications, 2004, 123(3): 479-496.
[3] Crespi G P, Ginchev I, Rocca M. Existence of solutions and star-shapedness in minty variational inequalities [J]. Journal of Global Optimization, 2005, 32(4): 485-494.
[4] Ivanov V I. Optimization and variational inequalities with pseudoconvex functions [J]. Journal of Optimization Theory and Applications, 2010, 146(3): 602–616.
[5] Liu Caiping, Yang Xinmin, Lee H W. Characterizations of the solution sets of pseudoinvex programs and variational inequalities [J]. Journal of Inequalities and Applications, 2011(1): 1-13.
[6] Weir T, Mond B. Preinvex functions in multiple objective optimization [J]. Journal of Mathematical Analysis and Applications, 1988, 136(1): 29-38.
[7] Ansari Q H, Rezaei M. Generalized pseudolinearity [J]. Optimization Letters, 2012, 6(2): 241-251.
[8] Mohan S R, Neogy S K. On invex sets and preinvex functions [J]. Journal of Mathematical Analysis and Applications, 1995, 189(3): 901-908.
[9] Sach P H, Penot J P. Characterizations of generalized convexities via generalized directional derivative [J]. Numerical Functional Analysis and Optimization, 1998, 19(5/6): 615-634.
[10] 王岗, 刘学文, 姜艮, 等. 一类变分不等式问题解集的刻画 [J]. 江西师范大学学报: 自然科学版, 2011, 35(4): 388-390.
[11] 肖红. 广义Minty似变分不等式解的性质 [J]. 西南大学学报: 自然科学版, 2010, 32(10): 126-131.
[12] 陈熙德. 自反Banach空间中一类变发不等式解的存在唯一性[J]. 重庆师范大学学报: 自然科学版, 1991, 16(2):44-48.

更新日期/Last Update: 1900-01-01