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Generalized Invexity and Generalized Invariant Monotonicity

In: Generalized Preinvexity and Second Order Duality in Multiobjective Programming

Author

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  • Xinmin Yang

    (Chongqing Normal University)

Abstract

A closely related concept of the convexity of a real-valued function is the monotonicity of a vector-valued function. It is well known that the convexity of a real-valued function is equivalent to the monotonicity of the corresponding gradient function. It is worth noting that monotonicity has played a very important role in the study of the existence and solution methods of variational inequality problems. As an important breakthrough, a generalization of this relation is given in [46] for various pseudo/quasi-convexities and pseudo/quasi-monotonicities.

Suggested Citation

  • Xinmin Yang, 2018. "Generalized Invexity and Generalized Invariant Monotonicity," Springer Optimization and Its Applications, in: Generalized Preinvexity and Second Order Duality in Multiobjective Programming, chapter 0, pages 77-91, Springer.
    • Handle: RePEc:spr:spochp:978-981-13-1981-5_5
    DOI: 10.1007/978-981-13-1981-5_5
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