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

Authors:
Ke Quan Zhao;Xue Wen Liu;Zhe Chen
Affiliations:
Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing, China 400047;Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing, China 400047;Department of Mathematics and Computer Science, Chongqing Normal University, Chongqing, China 400047
Venue:
Journal of Global Optimization
Year:
2011

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Abstract

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.