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.
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Yang, X. (2018). Generalized Invexity and Generalized Invariant Monotonicity. In: Generalized Preinvexity and Second Order Duality in Multiobjective Programming. Springer Optimization and Its Applications, vol 142. Springer, Singapore. https://doi.org/10.1007/978-981-13-1981-5_5
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DOI: https://doi.org/10.1007/978-981-13-1981-5_5
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