Convex function is an significant type of function.
凸函数是一类重要的函数。
Convex function plays an important role in mathematical programming.
凸函数在数学规划中具有十分重要的作用。
The loss functions are convex function and have risk optimize control stra...
证明了损失函数为凸函数，存在风险最优控制策略。
This article emphasizes important application of convex function in inequality proving.
本文着重论述了凸函数在不等式证明中的重要应用。
An application of the quality factor of convex function to chaotic signal analysis was given.
给出了凸函数品质因数在混沌信号分析中的应用实例。
The loss functions are convex function and have risk optimize control strategies have been proved.
证明了损失函数为凸函数，存在风险最优控制策略。
The semismooth function is applied to UV-decomposition by using finite convex functions UV-decomposition.
利用UV-分解理论，将半光滑函数应用到UV-分解中。
In this paper, several properties of convex function are generalized to the case of quasi convex function.
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, we give some criteria for convex function, strictly convex function and explicitly convex function.
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。
Convex function of demand, convex distribution of price and an optimal model for coexistence of multi-prices are established.
建立了商品销售中的凸需求函数，凸分布和多种价格并存的优化模型。
An integral property of the convex function is generalized, and the some integral inequalities of the convex function are given.
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。
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。
It is proved that the optimality conditions are also sufficient if the objective function is a convex function of the plastic limit bending moment.
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。
In this paper, We availed the property of geometic convex function generalized a kind of important sum inequality and obtained some new conclusions.
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。
There are convex function and concave function, Which are of expansive application in many aspects, especially in inequality proof and error estimate.
凸(凹)函数有很多特性，这些性质可广泛应用于不等式的证明及误差估计等方面。
The criterion or cost-function with respect to the complex tap-weight vector of the equalizer and to the error probability is strictly a convex function.
该准则或价值函数是关于均衡器抽头权矢量和误差概率的严格凹函数。
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.
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。
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.
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。
As applications of majorizing inequality of convex function of several variables, some majorizing inequalities of eigenvalue and singular value of matrix are obtained.
作为多元凸函数的控制不等式在矩阵方面的初步应用，获得了矩阵特征值和奇异值的简洁的控制不等式。
Under the assumption condition of taking target function as an uniform convex function. We have proved that the LRKOPT has the global convergence and partial superlinear convergence.
在目标函数为一致凸函数的假设条件下，证明了LRKOPT方法的具有全局收敛和局部超线性收敛性。
This paper discusses the relationship between quasi-concave and pseudo-convex in the generalized convex function in the Linear topological space and offers some conditions of equivalence.
讨论了线性拓扑空间上广义凸函数中的拟凸与伪凸之间的关系，并给出它们之间的一些等价条件。
The two - parameters weighted mean in defined and an inequality for two - parameters weighted mean of convex function is prove, they have generalized and improved the results in literatures.
提出了函数的双参数加权平均的定义，证明了一个凸函数的双参数加权平均不等式，加强和推广了有关文献中的结果。
According to the character of expected information, the article proposed a new ID3 algorithm of decision trees to reduce the complexity of computing expected information by the convex function.
根据ID3算法中信息增益计算原理的特点，利用上凸函数的性质提出一种新的改进的ID3算法，减少了信息增益的计算量，进而提高ID3算法中信息增益的计算效率。
The concept of the midpoint quasi-convex function is introduced, and some conditions are obtained to ensure that midpoint quasi-convex function is quasi-convex in the measurable function space.
本文提出了中点拟凸函数的概念，在可测函数空间中，给出了中点拟凸函数拟凸的若干个充分条件。
This paper investigates the existence of complex support functional of a convex function in complex linear spaces and the complex numerical ranges of the complex support functionals on a point.
采用子空间中支撑泛函延拓的方法，构造出在复线性空间任意点上的复支撑泛函；确定在同一支撑点上复支撑泛函的数值域，从而得到复支撑泛函具有唯一性的充分必要条件。
Using separation theorem of convex set and the time terminal value function equation, we obtain the determining method of optimal terminal time as well as the Maximum principle.
由凸集分离定理及终端时间阈值函数方程，我们获得了最大值原理及最优控制时间的确定方法。
A branch and bound methods is proposed for minimizing concave function over a convex.
本文介绍了求解凸集上凹函数最优解的一种分支定界方法。
Generalized support function is a very important concept in plane convex sets, it play a crucial role in discuss kinematic measure of convex sets.
广义支持函数是平面凸域的一个非常重要的概念，它在讨论凸域的包含测度问题中起关键的作用。
In this paper, a bundle method for the minimization of the convex nonsmooth function in point by point maximum is suggested.
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。
Assuming knowledge of extreme points, we develop bounds for associated convex combinations and improve bounds on the integer programming problems objective function and variables.
应用已有的极点理论，优化相伴凸组合的界并改进整数规划问题的目标函数及变量的界。
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