This paper defines a kind of derivative for real function on convex set which is in linear space. By means of the derivative we study convexity of function and obtain some decision theories.
本文对线性空间中的凸集上的实值函数定义一种导数，用其研究函数凸性，得到了上述三种凸函数的若干判定定理。
In the second we give the necessary and sufficient conditions for strict convexity of power function of exponential family in the discrete case.
在第二个问题中，我们给出了在离散的情形下，指数族势函数严凸的充分必要条件。
Objective function presents comparatively strong convexity and lesser local extreme values on wide scale which is favour of converging to optimized values.
由于较粗尺度下目标函数呈现较强的凸性及较少的局部极值，很有利于收敛至优化解。
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