等式约束

To solve the nonlinear 0-1 programming problem, it is transformed into an equivalent continuous nonlinear programming on the domain of [0, 1] by a nonlinear equality discrete constraint.

为了求解非线性0-1离散规划问题，通过非线性等式的"离散性约束"将其转化为[0， 1]区间上等价的连续变量非线性规划。

The module conversion for a kind of Max-min problems is given, namely, the Max-min problem with equality and inequality constraint is converted into convex problem with linear constraint, which provides theoretical basis for designing effective algorithms.

最后，给出一类极大极小问题的模型转化，把带等式、不等式约束的极大极小问题转化为带线性约束的凸规划问题，这为设计更为有效的算法提供了理论依据。

At present, although finite element methods is a kind of effective measures in analyzing metal plastically forming problems with friction, dynamic friction in the process of metal forming is substituted with static friction and constant frictional force as one of independent constraint conditions is transposed to equivalent node-load or FEM unit is divided into contact unit and inner unit in numerous studys and applications, so that it result in relative bad accuracy and awkward operation. These defects mostly attribute to the fact that FEM bases on the variational equality principles, however frictional constraint will actually result in variational inequality energy functional.

目前，应用于分析金属塑性成形的有限元法是一种有效的处理摩擦效应的定量计算方法，但是许多应用和研究是用常摩擦来代替金属塑性成形过程中的动态摩擦；把常摩擦力作为单独的约束条件移置到等效结点载荷上或把有限元单元划分成接触单元和内单元，这些将导致解的精度相对不高及实际操作不方便等一系列问题，产生这些不足的重要原因之一在于它的理论基础是变分等式原理。

The mathematic model of optimization allocation of tolerance values is established. In the model, the objective function of the optimization is production cost-tolerance function, and the constraints of the optimization are equation and inequation in the fifth chapter.

以加工成本—公差函数为目标函数，以第五章的等式和不等式约束为约束条件，建立了公差大小最优分配的数学模型；基于遗传算法研究了形位公差大小的最优分配方法。

Solving linear programming problems in a linear equation group inequalities or the condition of a linear function for the most value problem.

求解线性规划问题，即在一组线性不等式或等式组的约束条件下求某个线性函数的最值问题。

Mond - Weir type dual and Wolfe type dual for any dimension programming with equality and in inequality constrains is discussed.

在Banach空间中定义了ρ－不变凸的概念，讨论了具等式和不等式约束的任意维规划的Mond－Weir型对偶与Wolfe型对偶。

A general super memory gradient projection method was generalized to solve the nonlinear programming problems about the nonlinear equality constraints and in equality constraints by using general projection matrix.

利用广义投影技术，将求解无约束规划的超记忆梯度算法推广，建立了求解带非线性等式和不等式约束优化问题的一种超记忆梯度广义投影算法，并证明了算法的收敛性。

By using generalized projection matrix, conditions are given on the scalars in the three term-memory gradient direction to ensure that the three term-memory gradient projection direction is a descent direction. A new three term-memory gradient projection method for nonlinear programming with nonlinear equality and in-equality constraints is presented.

利用广义投影矩阵，对求解无约束规划的三项记忆梯度算法中的参数给一条件，确定它们的取值范围，以保证得到目标函数的三项记忆梯度广义投影下降方向，建立了求解非线性等式和不等式约束优化问题的三项记忆梯度广义投影算法，并证明了算法的收敛性。

Various efficient, convergent and robust algorithms have been developed for such a SCOP. However, a more general constrained optimization problem with not only logic AND but also OR relationships exists in many practical applications.

但是，在实际应用中有很多更一般的约束优化问题，其等式或不等式约束之间不仅包含逻辑&与&关系，而且还包含逻辑&或&关系，现有的针对标准约束优化问题的各种算法不再适用。

One is a large scale nonlinear programming model with equalities, the other is a more complicated NP hard and nonlinear compound 0-1 programming model. It is difficult for the existed algorithms to fulfill the demands of efficiency and size for the above problems. Two corresponding genetic algorithms are presented, in which several suitable genetic operations are constructed to make the optimization search process in the range of feasible solutions.

一个为大规模的带等式约束的非线性规划模型，另一个为更为复杂的带NP难解问题的混合非线性0-1规划，已有算法都难以满足上述两种问题的求解规模及效率的需要，我们给出了相应的遗传算法，确定了适当的遗传操作，使得问题的寻优过程始终都在可行解范围内进行，不仅提高了优化速度，而且有效地提高了优化效果。

The reasons of iron ions content overproof in grade Ⅱ desalting water system,such as variation water quality,contamination of regenerant , operation adjustment of pretreatment system and switching operation of bed were discussed.

对二级脱盐水系统中铁离子含量超标的原因，如来水水质发生波动、再生剂受到污染、预处理系统操作调整、床体运行切换等进行了论述。

You were hired to drum up new business, so go and do it.

公司雇你招徕新业务，你就做你的事好了。