【摘要】 利用非光滑分析工具,建立了拓扑向量空间中Clarke广义梯度的单调性与函数的广义univexity之间的关系。在广义univexity的假设下,考虑了非光滑向量似变分不等式问题与非光滑向量优化问题之间的关系。该结果对已有结果进行了推广。更多还原

【Abstract】 In this paper,we establish the relationship between the generalized monotonicity of the gradient in the sense of Clarke and the generalized univexity of a function in the metrizable topological vector space setting by using the nonsmooth analysis. Moreover,the relationship between the nonsmooth vector variational-like inequality problems and the nonsmooth vector optimization problems is considered under the assumption of the generalized univexity. The results extend existing ones.更多还原