注意编写7个不等式作为5个不必有序的决策变量的和太过繁琐了，因为在某些约束中，索引可能会覆盖索引值7。
Note that it would be too boring to write seven inequalities as a sum of five decision variables that are not necessarily in order, because in some constraints, the index may overlap the index 7.
证明了有关函数平均值的一个估值不等式，应用它推出了若干重要的不等式。
An inequality of estimate for function means is proved, and by using it some classical inequalities are proposed.
本文给出了需求量与存储量取离散值时的最佳订货量(或最佳存储量)的若干不等式。
Thi paper gives a few inequality of optimum ordering quantity (or optimum storage) when demand and storage take discrete value.
最后，利用择一性定理，获得了含不等式和等式约束的广义次似凸集值映射向量最优化问题的最优性条件。
Finally, the optimality conditions for vector optimization problems with set valued maps with equality and inequality constraints are obtained with it.
本文通过使用向量似变分不等式和半预不变凸函数来证明约束向量优化的弱极小值的存在性。
In this paper, We prove the existence of a weak minimum for constrained vector optimization problem by making use of vector variational-like inequality and semi-preinvex functions.
然后利用拉格朗日乘数法与隐函数定理，求出了使其中一不等式局部反向的临界值。
Furthermore, utilizing the Lagrange method of multipliers and the implicit theorem to work out the critical value which makes one of those inequality locally inverted.
给出了自共轭四元数矩阵的弱圈积的特征值的一些不等式。
Some inequalities of eigenvalues for weak cycle products of self-conjugate quaternion matrices are given.
本文延拓辅助原理的技巧，来研究一类广义集值强非线性混合似变分不等式。
The auxiliary principle technique is extended to investigate a class of generalized set-valued strongly nonlinear variational-like inequalities.
本文研究集值向量变分不等式的严格可行性与可解性之间的关系。
In this paper, we investigate the relationship of strict feasibility and solv - ability for the multivalued vector variational inequality.
讨论了关于集值映象的混合似变分不等式的解的存在性。
The existence of solutions for the mixed variational-like inequalities on multi-valued mapping was studied.
延拓辅助原理的技巧研究一类取非紧值的集值映象的广义强非线性混合似变分不等式。
The auxiliary principle technique is extended to study a class of generalized strongly nonlinear mixed variational-like inequalities for set-valued mappings without compact values.
得到H -空间中的一个新的极大极小定理和几个广义单调集值映象的变分不等式定理。
A new minimax theorem and some theorems for variational inequalities with generalized monotone multivalued mapping in H-spaces are obtained.
第三部分，利用辅助原理研究了广义集值非线性混合似变分不等式的解的存在性，收敛性及算法的稳定性。
In the last section, we introduce and study a class of variational-like inequalities by applying the auxiliary principle technique.
阐述了利用导数知识研究函数的单调区间、大值最小值等问题的基本方法，以及导数方法为解决某些不等式的证明、列求和等问题提供了捷径。
It explains some basic ways of how to use derivative to study monotonous zone in function, to calculate maximum and minimum, and how to solve some problems on inequality and number sequence, etc.
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。
As applications of majorizing inequality of convex function of several variables, some majorizing inequalities of eigenvalue and singular value of matrix are obtained.
研究了图的正规拉普拉斯矩阵特征值与图的坚韧度，并给出了它们之间的不等式关系。
In this paper, the eigenvalues of the normalized Laplacian and the toughness of graphs are studied and the relation of inequality between of them is given.
本文讨论了一般正定复矩阵的两个性质，给出了正定复矩阵特征值的界，并给出了正定复矩阵行列式的模满足的一个不等式。
In this paper, some inequalities about singular values of normal matrices are established by the properties of compound matrix and the relation between eigenvalue and singular value of matrix.
本文主要研究了非紧致集上的极大值函数和带不等式约束的广义半无限规划。
This dissertation is devoted to the study of sup-type function on non-compact set and the first-order optimality conditions for generalized semi-infinite programming with inequality constraints.
本文主要研究了非紧致集上的极大值函数和带不等式约束的广义半无限规划。
This dissertation is devoted to the study of sup-type function on non-compact set and the first-order optimality conditions for generalized semi-infinite programming with inequality constraints.
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