convex function

I generalized the convex function from special to general.

对函数凸性的推广遵循从特殊到一般的研究思路.

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。

The minimum entropy production object equation is established to realize the optimal planning of hydropower energy system power generation. Optimal solution of the object equation can be achieved demonstratively according to the convex programming principle and convex function property.

建立了系统电站发电量优化规划即熵增最小目标方程，应用凸规划原理及凸函数性质论证了目标方程存在最优解；

(α,β)-Type Almost Convex Function with Complex Number Order

复数阶（α，β）型近于凸函数

The Preliminary Research of Convex Function An Analysis of Cost Functions in High Education between China and Foreign Countries

凸函数初探中外高等教育成本函数研究

On h Convex Function

h凸函数

The training task involves optimization of a convex cost function: there are no false local minima to complicate the learning process.

算法的训练过程本质上是求解一个二次凸优化问题，不存在局部极值问题，从而避免使学习过程复杂化。

The penalization method is our main method and the main tools are the extension of the Bihari inequality and the Yosida approximation of the subdifferential operator of the convex function.

文中所使用的主要方法是罚则函数法，主要工具是Bihari不等式的一个推广形式及凸函数次微分算子的Yosida逼近。

Inverse Problems of Differential Mean Value Theorem for Convex Function

凸函数的微分中值定理的反问题

Experiments on springback in concave and convex edge flanging are carried out. Method of the mixed-level orthogonal test design is used to select the training sets from experiment data, and a radial basis function ( RBF) neural network model for springback is developed.

对薄板内凹、外凸翻边进行了回弹试验，借助混合水平的正交试验设计方法从试验数据中选择训练样本，建立了回弹的径向基函数神经网络模型。

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。

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。

We show that under appropriate conditions, the matrix sequence is convergent if the objective function is a strictly convex quadratic function.

我们证明在一定条件下，MBFGS算法用于求解严格凸二次函数极小值时产生的迭代矩阵序列是收敛的。

We prove that matrix convexity and matrix weak convexity are equivalent when the function is continuous, so the inverse proportion function is a matrix convex function.

在函数连续的情况下，矩阵凸性与弱凸性等价，从而反比例函数具有矩阵凸性。

The Property of Piecewise Smoothness of Moreau-Yosida Approximation for a Piecewise C~ 2 Convex Function

分片C~2凸函数Moreau-Yosida逼近的分片光滑性质

Application of Support Function of Convex Curve in the Vessel Cross-sectional Reconstruction

卵形线支撑函数在血管截面重建中的应用

Global convergence for the algorithm is established under the assumption that the objective function is bounded from below, The authors also generalize the algorithm to constrained convex optimization and obtain the convergence that is the same as unconstrained algorithm.

此外还把算法推广到约束凸规划问题，得到了与无约束问题同样的收敛结果，如果约束是线性的，则算法是数值可行的。

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。

This paper demonstrates that every point of a continuous derivable function f ( x) within ( a, b) is a convex point, f ( X) is a convex function, and they are mutual conditions.

本文证明了（a，b）内连续可导函数f（x）的每个点都是凸性点与f（x）是凸函数互为充要条件；