提出了显拟凸函数的若干新性质。
Some new properties of explicitly quasiconvex functions are presented in this paper.
给出了严格B -凸函数的一些性质。
In this paper, some properties of strictly B-Vex functions were introduced.
凸函数是一类重要的函数。
凸函数在数学规划中具有十分重要的作用。
Convex function plays an important role in mathematical programming.
本文着重论述了凸函数在不等式证明中的重要应用。
This article emphasizes important application of convex function in inequality proving.
研究半局部凸函数在多目标半无限规划下的对偶性。
The duality conditions for multiobjective semi-infinite programming with semilocally convex functions are given.
证明了损失函数为凸函数，存在风险最优控制策略。
The loss functions are convex function and have risk optimize control strategies have been proved.
给出了凸函数品质因数在混沌信号分析中的应用实例。
An application of the quality factor of convex function to chaotic signal analysis was given.
由于T几何凸函数的广泛性，故其结果具有重要价值。
These results are important because of extensiveness of T-geometrically convex functions.
本文引入了一类新的广义凸函数—强预拟不变凸函数。
In this paper, a new type of generalized convex functions—strongly prequasi-invex functions is introduced.
本文讨论了将凸函数的几个性质推广到拟凸函数的情形。
In this paper, several properties of convex function are generalized to the case of quasi convex function.
定义了模糊随机变量值凸函数概念，讨论了它的基本性质。
The concept of fuzzy random variable-valued convex functions is introduced.
研究了用束方法求解非光滑逐点最大凸函数的极小化问题。
In this paper, a bundle method for the minimization of the convex nonsmooth function in point by point maximum is suggested.
本文给出了凸函数，严格凸函数和显凸函数的一些判别准则。
In this paper, we give some criteria for convex function, strictly convex function and explicitly convex function.
利用凸函数或微积分中二阶导数符号可以直接给出一连串不等式。
That is, a succession of inequations can be obtained directly by using convex functions or quadratic derivative symbols in calculous.
本文首先归纳总结了凸函数的几个不同的定义，并说明其等价性。
In the first part of this paper, we gave several different definition of convex functions and equivalent proposition.
对函数族的包含关系及a级负系数调和凸函数族进行了一些研究。
Also, we has studied the inclusion relations to the class of analytic functions and harmonic univalent functions with negative coefficients.
在黎曼流形上分别给出了伪不变凸函数和弱向量似变分不等式的概念。
The definitions of pseudo-invex function and weak vector variation-like inequality on Riemannian manifolds are presented.
因此，对凸函数和广义凸函数的研究是数学规划中最重要的内容之一。
Therefore, the research on convexity and generalized convexity is one of the most important aspects in mathematical programming.
研究与凸函数对应的凹函数及其性质，并指出了凹函数在最优化中的应用。
In this paper, concave function and its properties are discussed. And concave function's application in optimization are shown as well.
然而，对一般非凸函数，PRP方法即使采用精确线搜索也不能保证全局收敛。
However, the PRP method even with the exact line search is not globally convergent on nonconvex functions.
给出了微分中值定理的一个推广形式，并将所得结果应用于凸函数性质的研究。
This article gives a spreading form of the mean value theorem of differential and applies the gained results to the quality of convex function.
给出了凸函数的一个积分性质的推广，并由此得到了凸函数的几个积分不等式。
An integral property of the convex function is generalized, and the some integral inequalities of the convex function are given.
本文导出了对数凸函数的又一性质，并利用该性质很方便地推导了一类不等式。
By using the q-exponential function and q-logarithm function, the analytical solution of the equation is derived.
文章利用几何凸函数的性质推广了一类重要的和式不等式，得到了一些新的结论。
In this paper, We availed the property of geometic convex function generalized a kind of important sum inequality and obtained some new conclusions.
本文用凸函数构造了线性次序统计量和线性秩统计量，并证明了它们的渐近正态性。
In this paper, we use the convex function to form the order statistic and the linear rank statistic, and the asymptotic normality of the statistics are proved.
当目标函数是塑性极限弯矩凸函数时，证明了这一最优性条件也是最优解的充分条件。
It is proved that the optimality conditions are also sufficient if the objective function is a convex function of the plastic limit bending moment.
在有效前沿上，风险是收益的严格单调递增凸函数，收益是风险的严格单调递增凹函数。
On the effect boundary, risk is return's rigid monotony increase by degrees convex function , return is risk's rigid monotony increase by degrees concave function.
文中引入了一类广义不变凸函数，对一类变分问题给出了最优解的充分性条件以及对偶理论。
The generalized invex functions are introduced and the optimality theorems and duality theory are established for a class of variational problems.
本文通过使用向量似变分不等式和半预不变凸函数来证明约束向量优化的弱极小值的存在性。
In this paper, We prove the existence of a weak minimum for constrained vector optimization problem by making use of vector variational-like inequality and semi-preinvex functions.
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