A Note on Nonsmooth Pseudoinvexity

Zhao et al has obtained a sufficient condition about semi-strictly prequasi-invex functions, which the differentiable pseudoinvex functions must be semi-strictly prequasi-invex functions with the same vetor-valued function under some suitable conditions. In this paper, it was generalized that the corresponding results to the nonsmooth case. It was proved that the nonsmooth pseudo-invex functions which based on the open invex set with respect to the vector-valued function and satisfied the condition of Lipschitz which are semi-strictly srequasi-invex functions with respect to the same vector-valued function by making use of the condition C and the theory of Clarke subdifferential.