查询词典 conjugate convex function

To use linear program, we have to take care of two problems. The first problem is that the actual relationship between intensity and duration is nonlinear convex function. In this study, we propose to use piece-wise linear curve to approximate the nonlinear convex curve. The second problem is that there are many feasible event sequences.

使用线性规划遭遇的困难有二：第一，作业强度与作业时间呈非线性之凸函数关系，因此本研究将使用片段线性曲线(piece-wise linear curve)近似作业强度与作业时间呈非线性之凸函数关系；第二，专案有很多组可能事件顺序，事件顺序的不同会产生不同的资源限制式，本研究提出一个系统化的方法求解问题。

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。

In this paper, we introduce the definition of convex function by the aid of convex set.

本文首先借助于凸集概念引出凸函数定义，揭示凸函数概念与凸性这一几何性质的联系。

Infinitely many convex functions with quality factors better than that of the convex function in entropy were discovered.

发现了品质因数比熵中凸函数更好的无穷多凸函数。

This paper is a discussion of new algorithm for convex objective function and convex programming with constraints.The algorithm is an extension and improvement for a new linear programming.

对一般凸目标函数和一般凸集约束的凸规划问题新解法进行探讨，它是线性规划一种新算法的扩展和改进。

In chapter 4 , with S-KKM mapping , a new Ky Fan\'s minimax inequality is proved , the locally convex H-space with uniform structure is introduced , s-HKKM mapping is defined as the generalization of KKM mapping, with the H-convexity of Hausdorff locally convex H-space , a new fixed point theorem for the compact andclosed mapping belonging to the class s-HKKM is established ;with local intersection property of muti-function ,K-H-quasi-convexity of mapping , connectedness of set and condensing correspondences, some new vector quasi-variational inequalities are established , respectively .

第四章利用S-KKM映射，建立了新的Ky Fan极小极大不等式；定义了带有一致结构的局部凸H-空间，利用Hausdorff局部凸H-空间的H-凸性，对于属于s-HKKM中紧的闭映射建立了新的不动点定理，利用对应的局部交性质、映射的K-拟-凸性、集合的连通性以及φ-condensing对应分别建立了相应的拟向量变分不等式。

And based on this result, we also prove the connectedness of G-properly efficient solution set when the vector objected function is both like-convex and quasi-convex.

在此基础上，还得到向量目标函数既似凸又拟凸的多目标最优化问题G-恰当有效解集是连通的结论。

Moreover, we get the sufficient and necessary condition of in Orlicz spaces.Chapter 3 Extreme points and strongly extreme points in Orlicz spaces equipped with the generalized Orlicz norm: In this paper, the conceptions of the generalized Orlicz norm and the generalized Luxemburg norm are introduced, and the criteria of extreme points and strongly extreme points of Orlicz function spaces equipped with the generalized Orlicz norm are obtained. Moreover, criteria of space strictly convex and mid-point locally uniform convex are given.

第三章 赋广义Orlicz范数的Orlicz函数空间的端点和强端点：本章在Orlicz空间推广了Orlicz范数和Luxemburg范数，引入了广义Orlicz范数和广义Luxemburg范数的定义，并给出了赋广义Orlicz范数的Orlicz函数空间的端点和强端点的判据，进而得到了赋广义Orlicz范数的Orlicz函数空间严格凸和中点局部一致凸的充要条件。

Optimization; parametric quadratic convex programming; set-valued map; directional derivative; linear stability; solution-set map; parametric linear programming; error bound; subdifferential map; lower locally directionally Lipschitzian; upper locally di-rectionally Lipschitzian; locally directionally Lipschitzian; convex function; quasidiferential; kernelled quasidiferential; quasi-kernel; star-kernel; star-diferential; Penot diferential; subderivative; superderivative; epiderivative; set-valued optimization; set-valued analysis; subdifferential; optimization condition;ε-dual; scalization; generalized subconvexlike-cone;ε-Lagrange multiplier

基础科学，数学，运筹学最优化；集值映射；方向导数；线性稳定；最优解集映射；参数线性规划；参数凸二次规划；误差界；次微分映射；下局部方向Lipschitzian；上局部方向Lipschitzian；局部方向Lipschitzian；凸函数；拟微分；核拟微分；拟核；星核；星微分； Penot-微分；上导数；下导数； Epi-导数；集值优化；集值分析；集值映射的次微分；最优性条件；广义锥次类凸；ε-对偶；数乘；ε-Lagrange乘子

When using restricted maximum likelihood for parameter estimation, we need to get the minimum of a function. But if the expression of the function is complicated, it is difficult to obtain the derivatives of the function. We introduced conjugate direction method which avoided the derivatives.

在用限制极大似然法估计参数时，需解决函数的极小化问题，而当函数的表达式较为复杂时，将难以获得其偏导数，本文给出的共轭方向法，避开了求导问题。

The dissecting of samples in group2 were difficult. The root of pulmonary artery and ascending aorta failed to be unfolded because fibrous tissue was tough, right and left fibrous trigone were too firm to be solved by hand. Cardiac muscle fibers couldn't be stripped along myofibrillar trajectory since they were prone to break because of their friability.

组2的心脏解剖困难，表现为纤维组织坚韧，游离肺动脉非常困难；徒手无法松解左、右纤维三角，肺动脉和主动脉根部的游离非常困难；心肌纤维坚硬、质脆，解剖时容易断离成碎块，无法沿纤维走行方向剥离。

We have battled against the odds in a province that has become increasingly violent.

我们对在一个争夺日益激烈省的可能性。