共轭凸函数

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.

提出的算法是利用凸函数共轭性质中的Young不等式构造优化目标函数，这个优化目标函数对于权值和隐层输出来说为凸函数，不存在局部最小。

Generalized strong vector variational-like inequalities; Minty's lemma; KKM mapping; pseudomonotone; Ky Fan lemma; open mapping theorem; complete; the second category; conjugate; proper convex lower semicontinuous function; linear mapping; closedness

基础科学，数学，数学分析广义强向量似变分不等式； Minty引理； KKM映象；伪单调； Ky Fan引理；开映射定理；完备；第二纲；共轭；真凸下半连续函数；线性映射；闭性

The decreasing conditions of an energy function are investigated by the use of convex function. By utilization of the primal convex function, the conditions are analyzed under which its conjugate function minus a quadratic function is also convex.

利用凸函数的定义研究了能量函数下降的条件，根据凸函数的性质分析它的共轭函数减去二次函数之差仍为凸函数的条件。

In this paper, based on the conjugate function and the dual programming of convex programming, with the dual cone, to conic programming, the dual programming is fully discussed, the expression of the dual programming is educed, the main dualities are proved, and the dualities of the familiar conic programming are studied.

以共轭函数和凸规划的对偶规划为基础，利用对偶锥的概念，全面讨论了一般锥规划的对偶问题，严格推导出锥规划对偶规划的表示形式，给出了锥规划的主要对偶性质，并用这些结果研究了常见锥规划的对偶性。

The decreasing conditions of an energy function are investigated by the use of convex function.

利用凸函数的定义研究了能量函数下降的条件，根据凸函数的性质分析它的共轭函数减去二次函数之差仍为凸函数的条件。

By weakening the premise of the convexity of the objective function required in paper[7], we prove the sufficient desent property and the global convergence with the strong Wolfe line search.

在第二章中，我们参照文献[7]中的方法，提出了一类与HS算法相关的共轭梯度算法，并减弱了文[7]中要求目标函数二阶连续可微且为凸的前提条件，采用强Wolfe线搜索，在较弱的条件下证明了这一类算法具有充分下降性和全局收敛性。

By level function,ε-subdifferential, normal cone and dual function, global optimal solutions for a convex function in locally convex topological vector space and a few of equivalent forms on it are obtained. Maximum points are characterized.

讨论局部凸拓扑向量空间中凸函数的全局最优解，用水平函数、ε-次微分及法向锥和共轭函数等工具刻画其最大值点，得到最优解的几个等价形式。

Secondly,in metrizable topological vector spaces,the results for linear maps with complete graphs is an open mapping are presented.

在第三章，我们研究了在赋范空间中，真凸下半连续函数与线性映射结合的共轭公式的推广。

Consequently, when applied to minimize a strictly convex quadratic function, the proposed methods terminate at the solution of the problem finitely.

因此，当目标函数是严格凸的二次函数，且采用精确线性搜索时，这些修正的共轭梯度法具有共轭性和二次终止性。

Duality is emphasized throughout,particularly in the form of Fenchel's conjugacy correspondence for convex functions.

贯穿本书的各个部分，对偶始终是被强调，尤其是在凸函数的 Fenchel 共轭理论的形式部分。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。