半(E,F)—凸函数的一些新性质

Some New Properties of Semi-(E,F)-Convex Functions

基于(E,F)—凸函数,得到了半(E,F)—凸函数。引入次线性函数,利用半(E,F)-凸函数的定义,研究了次线性函数与半(E,F)—凸函数复合后的半(E,F)—凸性,半(E,F)—凸函数水平集的性质;研究了在半(E,F)—凸性的务件下极小值点存在的充要务件,并从变分不等式的角度对该充要条件作了全新的证明,且给出了另一个等价条件。

Based on the （E, F）-convex function, the semi- （E, F）-convex function is obtained, in order to further improve the properties of semi-（E,F）-convex function, the application of semi- （E, F）-convex function is defined constraints reduce,research which can be better applied in optimization problems. Firstly,introduced a linear function, using the definition of semi- （E,F）-convex function,studied the linear function and after the semi- （E, F）-convex function composite semi-convexity, the properties of semi-（E, F）-convex function of the level set,and studied under the condition of semi-（E,F）-convex sufficient and necessary condition for the existence of minimum point. In order to obtain the necessary and sufficient conditions for existence of the minimum point, make a new proof of the necessary and sufficient conditions of the variational inequality, and another equivalent condition is given.