A class of r-semipreinvex functions and optimality in nonlinear programming
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- Zhao, K.Q., Liu, X.W. & Chen, Z. J Glob Optim (2011) 49: 37. doi:10.1007/s10898-010-9532-x
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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.