Please wait a minute...
北京大学期刊网 | 作者  审稿人  编委专家  工作人员

首页   |   关于   |   浏览   |   投稿指南   |   新闻公告
数学进展 - 2016, Vol. 45(2): 289-298
Vector Optimization With Cone Constraints Under Generalized Type I Univexity in Banach Spaces

JIAO Hehua1, LIU Sanyang2

1. 长江师范学院数学与统计学院, 重庆, 408100;
2. 西安电子科技大学数学与统计学院, 西安, 陕西, 710071
1. School of Mathematics and Statistics,Yangtze Normal University, Chongqing, 408100, P. R. China;
2. School of Mathematics and Statistics, Xidian University, Xi'an, Shaanxi, 710071, P. R. China

收稿日期: 2014-07-24
出版日期: 2016-03-10
2016, Vol. 45(2): 289-298
DOI: 10.11845/sxjz.2014114b

[176 KB]

    /   /   推荐

摘要 本文在巴拿赫空间中为一类带锥约束的向量优化问题引入了一些$\alpha$-d I型一致不变凸函数的新概念.建立了一些 Karush-Kuhn-Tucker型最优性充分条件.而且建立了一个Mond-Weir型对偶, 在各种$\alpha$-d I型一致不变凸性条件下得到了弱对偶、强对偶和逆对偶定理.
Abstract:In this paper, we introduce new concepts of $\alpha$-d-type I univex functions between Banach spaces for a vector optimization problem with cone constraints. We establish some Karush-Kuhn-Tucker type sufficient optimality conditions for a feasible point to be a weakly efficient (or an efficient) solution. Moreover, a Mond-Weir type dual is formulated and weak, strong and converse duality results are obtained under various types of $\alpha$-d-type I univexity assumptions.
PACS:  O221.6  
[1]Antczak, T., Optimality conditions and duality for nondifferentiable multiobjective programming problems involving d-r-type I functions, J. Comput. Appl. Math., 2009, 225(1): 236-250.
[2]Batista dos Santos, L., Osuna-Gòmez, R., Rojas-Medar, M.A. and Rufiàn-Lizana, A., Preinvex functions and weak efficient solutions for some vectorial optimization problem in Banach spaces, Comput. Math. Appl., 2004, 48(5/6): 885-895.
[3] Bazaraa, M.S., Sherali, M.S. and Shetty, C.M., Nonlinear Programming: Theory and Algorithms, 3rd Ed., New York: Wiley, 2006.
[4]Chen, J.W., Cho, Y.J., Kim, J.K. and Li, J., Multiobjective optimization problems with modified objective functions and cone constraints and applications, J. Global Optim., 2011, 49(1): 137-147.
[5]Craven, B.D., Control and Optimization, London: Chapman and Hall, 1995.
[6] Hachimi, M. and Aghezzaf, B., Sufficiency and duality in nondifferentiable multiobjective programming involving generalized type I functions, J. Math. Anal. Appl., 2006, 319(1): 110-123.
[7]Hanson, M.A. and Mond, B., Necessary and sufficient conditions in constrained optimization, Math. Program., 1987, 37(1): 51-58.
[8]Hanson, M.A., Pini, R. and Singh, C., Multiobjective programming under generalized type-I invexity, J. Math. Anal. Appl., 2001, 261(2): 562-577.
[9]Jayswal, A., On sufficiency and duality in multiobjective programming problem under generalized $\alpha$-type I univexity, J. Global Optim., 2010, 46(2): 207-216.
[10]Jayswal, A. and Kumar, R., Some nondifferentiable multiobjective programming under generalized d-V-type-I univexity, J. Comput. Appl. Math., 2009, 229(1): 175-182.
[11]Kuk, H. and Tanino, T., Optimality and duality in nonsmooth multiobjecive optimization involving generalized type-I functions, Comput. Math. Appl., 2003, 45(10/11): 1497-1506.
[12]Mangasarian, O.L., Nonlinear Programming, New York: McGraw-Hill, 1969.
[13] Mishra, S.K. and Noor, M.A., Some nondifferentiable multiobjective programming problems, J. Math. Anal. Appl., 2006, 316(2): 472-482.
[14] Mishra, S.K., Wang, S.Y. and Lai, K.K., Nondifferentiable multiobjective programming under generalized d-univexity, European J. Oper. Res., 2005, 160(1): 218-226.
[15] Mond, B. and Weir, T., Generalized concavity and duality, In: Generalized Concavity Optimization and Economics (Schaible, S. and Ziemba, W.T. eds.), New York: Academic Press, 1981, 263-280.
[16]Noor, M.A., On generalized preinvex functions and monotonicities, J. Ineq. Pure and Appl. Math., 2004, 5(4): Article ID 110, 20 pages.
[17] Slimani, H. and Radjef, M.S., Nondifferentiable multiobjective programming under generalized $d_{I-invexity, European J. Oper. Res., 2010, 202(1): 32-41.
[18]Suneja, S.K., Srivastava, M.K., Optimality and duality in nondifferentiable multiobjective optimization involving d-type I and related functions, J. Math. Anal. Appl., 1997, 206(2): 465-479.
[19]Yu, G.L. and Liu, S.Y., Some vector optimization problems in Banach spaces with generalized convexity, Comput. Math. Appl., 2007, 54(11/12): 1403-1410.
[20]Zhang, W.Y., Xu, S. and Li, S.J., Necessary conditions for weak sharp minima in cone-constrained optimization problems, Abstr. Appl. Anal., 2012, 2012: Article ID 909520, 11 pages.
No related articles found!
Full text



首页 · 关于 · 关于OA · 法律公告 · 收录须知 · 联系我们 · 注册 · 登录

© 2015-2017 北京大学图书馆 .