凸函数

新方法中将LMS算法中的各步权增量向量旋转后放至同一平面，在此基础上利用凸函数外推法求出计算步长的当前最佳估计值。

In the new method the increment of the weights vector in previous steps was rotated and placed to a plane , then the extended method for a one variable convex function was used .

B0型空间上共轭凸函数的指数共轭性

Conjugate properties of exponent of conjugate convex function on B_0-type spaces

本文首先在Fuzzy值集上建立了Fuzzy凸函数的概念，在此基础上研究了Fuzzy正项几何规划的有关性质。

This paper establishes the conceptions of Fuzzy convex function on the Fuzzy value set .

Rn~+上凸函数的严格凸与限制增长性

Strict Convex and Moderate Increment of Convex Function on R + n

（h，φ）-凸函数的广义方向导数及其性质

Generalized Directional Derivative of ( h ;φ) - Convex Function and its Properties

结果表明，分子片的能量函数E（N）是凸函数。

It is shown that the energy curve of the molecular fragments is convex .

h凸函数性质的推广

Properties of h - convex function

E凸函数的次微分

Subdifferentials of E - convex functions

胡克教授在此问题上作了一系列的研究，对于近于凸函数的K次对称函数得到了问题的解答。

Professor HU KE has studied this problem , and obtain the answer on close-to-convex function .

r凸函数的运算性质

Operation properties of r-convex functions

h凸函数

On h Convex Function

非光滑（F，α，ρ，d）-凸函数的多目标分式规划最优性条件

Optimality Conditions for Nonsmooth Multiobjective Fractional Programming with Nonsmooth ( F ,α,ρ, d ) - Convexity

〕，其中F（x）就是本文中所定义的一个函数，C为常数，ε为任意正数，从而得到了一类推广的凸函数。

F ( x ) is the defined function . C is a constant and e is any positive number .

同时，当h（y）为严格下凸函数时，给出了类似的定理B。

Meanwhile , when h ( y ) is a strictly lower convex function , we also give the similar theorem B.

A.Youness提出的结论，并据此把凸函数的一些性质推广到E凸函数。

The author has corrected the result of Theorem 3.1 and extended some properties of convex functions to E-convex functions .

广义凸函数是凸函数的推广，它包括伪凸函数，拟凸函数和r凸函数等。

Generalized convex function is a generalization of convex func-tion , including pseudoconvex function , quasiconvex function , r-convex function , etc.

B凸函数下多目标规划的Mond-Weir对偶和Wolf对偶

Mond Weir Duality and Wolf Duality Multiobjective Programming for B vex

第二章：作者引入了一定义在单位开圆内新的解析函数类K（λ，β），它是β型近于凸函数的K（β）的推广。

In the second chapter : The author introduces certain class of analytic function K (λ,β) defined in the open unit disc .

通过引进r-凸函数的概念，得到了在适当的限制条件下凸函数是r–凸函数的结论。

The conclusions that in proper restricted conditions , convex functions are r-convex functions were reached by introducing the conception of r-convex function .

在（F，ρ）s-凸函数的基础上，给出了多目标规划的两个逆对偶定理。

On the basis of ( F ,ρ) _s Convex functions two converse dual theorems of multiobjective programming are given under .

Hilbert空间上凸函数的上、下指数的共轭性质

Conjugate Properties of the Super ( Lower ) Exponent Convex Function on Hilbert Spaces

凸函数的某些性质及其在凸损失下Bayes估计中的应用

On some properties of convex functions and their applications in Bayes estimation with the convex loss

该文利用凸函数共轭性质中的Young不等式构造前馈神经网络优化目标函数。

This paper presents a new algorithm for feed forward neural networks based on a new optimal target function constructed according to Young inequality in the conjugate of convex function .

关于f，θ的ρ-弧式凸函数的Kuhn-Tucker条件

On the Kuhn-Tucker Conditions of ρ - Arcwise Convex Function to f , θ

凸函数的Hadamard不等式的若干推广

On Some Extentions of Hadamard Inequalities for Convex Functions

对数凸函数的Jensen型和Hadamard型不等式

Jensen type and Hadamard type inequalities of logarithmic convex function

近于凸函数的Hadamard乘积

On the Hadamard Products of Close-to-convex Functions

第二章介绍了没有明确线性结构的P型空间。包括P型空间中的半凸集和凸集，P型空间中的凸函数和拟凸函数。

In Part two , we introduce the concept of P-spaces without imposing any explicitly stated linear structure and some notions in P-spaces including half convex sets , convex sets , convex functions and quasi-convex functions .

E凸函数、半E凸函数、拟半E凸函数及伪半E凸函数都是对凸函数的推广，即它们都是广义的凸函数。

E-convex function , semi - E-convex function , quasi-semi - E-convex function and pseudo-semi - E-convex function are all the generations of convex function , i. e , generalized convex functions .

Banach空间中连续凸函数的Gateaux可微性的一个注记（英文）

A Note To Gateaux Differentiability Of Convex Continuous Function On Banach Space ;