On non-smooth α-invex functions and vector variational-like inequality

In this paper, we establish some relationships between vector variational-like inequality and non-smooth vector optimization problems under the assumptions of alpha-invex non-smooth functions. We identify the vector critical points, the weakly efficient points and the solutions of the weak vector variational-like inequality, under non-smooth pseudo-alpha-invexity assumptions. These conditions are more general than those of existing ones in the literature. In particular, this work extends an earlier work of Ruiz-Garzon et al. (J Oper Res 157: 113-119, 2004) to a wider class of functions, namely the non-smooth pseudo-alpha-invex functions. Moreover, this work extends an earlier work of Mishra and Noor (J Math Anal Appl 311: 78-84, 2005) to non-differentiable case.