全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

(h,φ)-凸函数与(h,φ)-Lipschitz函数的一些广义微分性质

Keywords: 广义凸函数,广义Lipschitz函效,导数,次微分,次梯度,梯度

Full-Text   Cite this paper   Add to My Lib

Abstract:

利用函数f与它的对应函数f(t)=φ(f(h~(-1)(t)))之间的关系,研究了(h,φ)-凸函数和(h,φ)-Lipschitz函数的广义方向导数,得到了R~n上连续(h,φ)-凸函效的广义方向导数的有限性、上半连续性以及估值不等式.在f是R~n上的(h,φ)-凸函数的假设下,给出了f为局部(h,φ)-Lipschitz的一个充分必要条件.并讨论了R~n上的(h,φ)-凸函数和(h,φ)-Lipschitz函数的关系,得到了(h,φ)-凸函数的广义次微分的几个基本性质.

References

[1]  徐义红,刘三阳.(h,φ)-Lipschitz函数及其广义方向导数和广义梯度[J].数学物理学报,2006,26A(2):212-222.XU Yi-hong,LIU San-yang.The (h,(?))-Lipschitz function,its generalized directional derivative and generalized gradient [J].Acta Mathematica Scientia,2006,26A(2):212-222.(in Chinese)
[2]  AUBIN J P.Optima and equilibria:an introduction to nonlinear analysis [M].Berlin:Springer-Verlag,1993.
[3]  徐义红,刘三阳.(h,φ)-不变广义凸函数的若干性质与(h,φ)-不变广义凸多目标规划的最优性及对偶性[J].应用数学学报,2003,26(4):726-736.XU Yi-hong,LIU San-yang.Some properties for (h,(?))-generalized invex functions and optimality and duality of (h,(?))- generalized invex multiobjective programming[J].Acta Math Appl Sinica,2003,26(4):726-736.(in Chinese)
[4]  BEN-TAL A.On a generalized means and generalized convex functions [J].J Optim Theory Appl,1977,21:1-13.
[5]  张庆祥.非光滑(h,φ)-半无限规划解的充分性和对偶性[J].应用数学学报,2001,24(1):129-138.ZHANG Qing-xiang.On sufficiency and duality of solutions for nonsmooth (h,(?))-semi-infinite programming[J].Acta Math Appl Sinica,2001,24(1):129-138.(in Chinese)
[6]  NGAI H V.Extensions of fréchetε-subdifferential calculus and applications[J].J Math Anal Appl,2002,268:266-290.
[7]  FABIAN M.Subdifferentiability and trustworthiness in the light of a new variational principle of borvcein and preiss[J]. Acta Univ Carolina,1989,30:51-56.
[8]  AVRIEL M.Nonlinear programming:analysis and methods[M].New Jersey:Prentice-Hall,Englewood Cliffs,1976.
[9]  徐义红.(h,φ)-凸函数的广义方向导数及其性质[J].南昌大学学报(工科版),2002,24(4):81-84.XU Yi-hong.Generalized directional derivative of (h,(?))-convex function and its properties [J].Journal of Nanchang University(Engineering & Te(?)hnology),2002,24(4):81-84.(in Chinese)
[10]  CLARKE F H.Optimization and nonsmooth analysis[M].New York:Wiley-Interscience,1983.
[11]  YUAN De-hui,CHINCHULUUN A,LIU Xiao-ling,et al.Generalized convexies and generalized gradients based on algebraic operations[J].Journal of Mathematical Analysis and Applications,2006,321:675-690.
[12]  ROCKAFELLAR R T.Convex analysis[M].New Jersey:Princeton Press,1970.
[13]  WEIR T,MOND B.Pre-invex functions in multiple objective optimization[J].Journal of Mathematical Analysis and Applications,1998,136:29-38.
[14]  PHU H X.Strictly and roughly convexlike functions[J].J Optim Theory Appl,2003,117:139-156.
[15]  PASTOR K.Convexity and generalized second-order derivatives for locally Lipschitz functions [J].Nonlinear Analysis, 2005,60:547-555.
[16]  ERDOGAN A T.A low complexity multicarrier PAR reduction approach based on subgradient optimization [J].Signal Processing,2006,86:3 890-3 903.
[17]  SOLEIMANT-DAMANEH M.Characterization of nonsmooth quasiconvex and pseudoconvex functions [J].J Math Anal Appl,2007,330:1 387-1 392.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133