Journal of Global Optimization

, Volume 49, Issue 1, pp 37–47

A class of r-semipreinvex functions and optimality in nonlinear programming


DOI: 10.1007/s10898-010-9532-x

Cite this article as:
Zhao, K.Q., Liu, X.W. & Chen, Z. J Glob Optim (2011) 49: 37. doi:10.1007/s10898-010-9532-x


In this paper, a class of functions, named as r-semipreinvex functions, which is generalization of semipreinvex functions and r-preinvex functions, is introduced. Example is given to show that there exists function which is r-semipreinvex function, but is not semipreinvex function. Furthermore, some basic characterizations of r-semipreinvex functions are established. At the same time, some optimality results are obtained in nonlinear programming problems.


Semi-connected setsSemipreinvex functionsr-Semipreinvex functionsOptimalityNonlinear programming

Mathematics Subject Classification (2000)


Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceChongqing Normal UniversityChongqingChina