接着，利用函数的上次微分构造了不可微向量优化问题（VP）的广义对偶模型，并且在适当的弱凸性条件下建立了弱对偶定理。
Finally, the generalized dual model of the problem (VP) is presented with the help of upper subdifferential of function, and a weak duality theorem is given.
本文研究一类广义负系数单叶解析函数，得到了准确的系数估计，偏差定理，凸性半径和星形性半径。
In this paper, we study a generalized class of univalent functions with negative coefficients. Sharp coefficient estimates, distortion theorem and radius of convexity and starlikeness are obtained.
用集合的近似凸性研究函数的拟凸性。
Quasiconvex functions are studied by applying nearly convexity of sets.
用集合的近似凸性研究函数的拟凸性。在较弱假设下，获得了拟凸性的一些等价条件。
Quasiconvex functions are studied by applying nearly convexity of sets. Under weaker assumptions, some equivalent conditions for quasiconvexity are derived.
用集合的近似凸性研究函数的预不变凸性，在较弱的假设下获得了预不变凸性的一些等价条件。
Preconvex functions are studied by applying nearly convexity of sets in this paper. Under weaker assumptions, some equivalent conditions for preconvexity are derived.
函数的凸性与广义凸性在数学规划以及最优化理论中起着非常重要的作用。
Convexity and generalized convexity of functions play an important role in mathematical programming and optimal theory.
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。
Objective function presents comparatively strong convexity and lesser local extreme values on wide scale which is favour of converging to optimized values.
对求解最优化问题的极大熵方法中的关键函数——K- S函数的一致不变凸性作了讨论，得出“K-S函数是一致不变凸的，则一定是不变凸的”结论。
It was discussed that the consistent invexity of K S function which is the key function used by maxinum entropy method in optimization problems solution.
证明该算法在目标函数为一致凸时具有局部超线性收敛性。
It was proved that, when the objective function was uniformly convex, this algorithm possessed superlinear convergence.
一是函数的拟凸性、伪凸性及其次微分的拟单调性、伪单调性；
One is quasi-convexity and pseudo convexity of functions and quasimonotonicity and pseu-domonotonicity of their sub differentials .
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。
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.
锥拟凸向量函数的概念是通常实值函数拟凸性的拓广。 由于拓广途径不一，在许多有关文献中各自提出了自己的锥拟凸向量函数概念。
This paper summarizes several different definitions of cone quasiconvex vector functions proposed in different literatures and discusses the relations among them.
本文提出了基于函数凸性的变换区域舍选法算法，该方法可应用于产生具有凸性区间的密度函数随机数。
A domain transformation method based on the property of convex is proposed and its basic properties are given.
研究了函数的一阶及二阶右导数与函数凸性的关系，推广了数学分析中的有关结果。
Then it expands the B-vex functions by defining connected pseudo B-vex and connected quasi B-vex functions in terms of right upper derivative with respect to an arc.
此类新类型的函数是凸性的推广。
利用差商代替难以计算的精确导数，结合既约梯度法的思想建立新的算法；在目标函数一致凸的条件下证明了既约差商法的整体收敛性。
The difference coefficient was used to replace the exact derivative which is difficult to be computed, and a new algorithm was presented by using the idea of reduced gradient method.
对于一般的非凸函数，其方向导数不具备任何凸性，可以利用一般正齐次函数的回收函数来给出它的一个上凸近似。
We research on describing preinvexity of functions in this paper by means of the density and weakly near convexity in the set.
利用集合的稠密性和弱近似凸性，进一步刻画函数的预不变凸性。
We research on describing preinvexity of functions in this paper by means of the density and weakly near convexity in the set.
研究了函数的一阶右导数与函数凸性的关系，给出了二个定理，把曲线凸性判定定理加以推广。
This paper discusses the relationship between the 1-stage progressive derivative and function convex, and two principles are presented, the curve convex judging principle is finally extended.
对PWA模型的状态区域进一步的细化凸划分，以增加找到分段二次lyapunov函数的可能性，减低闭环系统稳定性分析的保守性。
Further convex partitioning of the state's regions increases the possibility of finding the piece-wise quadratic Lyapunov functions, which reduces the conservativeness of the stability analysis.
对PWA模型的状态区域进一步的细化凸划分，以增加找到分段二次lyapunov函数的可能性，减低闭环系统稳定性分析的保守性。
Further convex partitioning of the state's regions increases the possibility of finding the piece-wise quadratic Lyapunov functions, which reduces the conservativeness of the stability analysis.
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