| 1. | On a class of quadratic programming problem with equality constraints
一类带有等式约束的二次规划问题 |
| 2. | Linear equality constraints
线性等式约束 |
| 3. | The method can be applied to the transportation problem with fuzzy equality constraints
用该方法求解了具有模糊等式约束的运输问题。 |
| 4. | Descending dimension algorithm for multi - objective programming with linear equality constraints
线性等式约束多目标规划的一个降维算法 |
| 5. | A global optimization algorithm for solving nonlinear programming problem involving many equality constraints
含有等式约束非线性规划的全局优化算法 |
| 6. | Mathematical programs with equilibrium constraints is a kind of specail opti - mzation problem , which besides equality constraints and inequality constraints it also contain complementarity constraints
带有均衡约束的数学规划问题( mathematicalprogramswithequilibriumconstrains ，缩写为mpec )是一类特殊的最优化问题，它的约束函数除了一般的等式和不等式约束之外，还包含有互补约束条件 |
| 7. | To the inequality constrained least squares adjustment problem , this paper converts many inequality constraints into one equality constraint by using aggregate function of non - linear programming ; a basic augmented lagrangean algorithm can obtain the solutions for equality constrained non - linear programming problem and the solutions are identical to those obtained by the bayesian method and / or simplex algorithm
摘要对不等式约束最小二乘平差问题，借助非线性规划中的凝聚约束方法把多个不等式约束转化为一个等式约束，采用拉格朗日极值法求解，解与贝叶斯解或单纯形解一致。 |
| 8. | By introducing the concepts of constraints measure and feasible degree , the extent to which the decision variables subject to the inequality constraints and equality constraints is described and then the self - adaptive penalty function is constructed , whose values are adaptively changed with the constraints feasible degree
该策略通过引入约束可行测度、可行度等概念来描述决策变量服从于不等式约束和等式约束的程度，并以此构造处理约束条件的自适应惩罚函数，惩罚值随着约束可行度的变化而动态自适应地改变。 |
| 9. | For applying the hybrid optimization algorithm to solve the optimization problem with constraints , a self - adaptive penalty strategy for handling the constraints is designed , which is used to convert the optimization problem with inequality constraints and equality constraints to the one only with the upper and lower bound constraints of the decision variables
为了便于应用混合优化算法对约束优化问题进行求解，设计了一种处理约束条件的自适应惩罚策略，用于将具有不等式约束和等式约束的优化问题转变为仅包含决策变量上、下限约束的优化问题。 |
| 10. | Finally , an algorithm for nonlinear multiobjective programming with linear equality constraints is offered . at first , multiobjective programming is transformed into a single - objective programming by using linear qualitied method ; and then , a single - objective programming with equality constraints is transformed into a series of linear equation systems , an algorithm is obtained by applying the dimension - descending algorithm with equality constraints
最后，获得了具有线性等式约束的非线性多目标规划问题的一种新算法，首先利用线性加权和法将线性等式约束的非线性多目标规划问题转化为单目标规划问题，再将其转化为求解一系列线性方程组，从而用降维算法获得了该问题的一个算法。 |
