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

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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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Chongqing Normal University, 400047, Chongqing, China

    Ke Quan Zhao, Xue Wen Liu & Zhe Chen

Authors
  1. Ke Quan Zhao
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  2. Xue Wen Liu
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  3. Zhe Chen
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Corresponding author

Correspondence to Ke Quan Zhao.

Additional information

This work is partially supported by the National Science Foundation of China (Grant 10771228), Research Grant of Chongqing Key Laboratory of Operations Research and System Engineering, and Research Grant of Chongqing Normal University (Grant 08XLQ01).

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Zhao, K.Q., Liu, X.W. & Chen, Z. A class of r-semipreinvex functions and optimality in nonlinear programming. J Glob Optim 49, 37–47 (2011). https://doi.org/10.1007/s10898-010-9532-x

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  • DOI: https://doi.org/10.1007/s10898-010-9532-x

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