We present and analyze a modified penalty functions ( mpf ) method for solving constrained optimization problems with inequality constraints . this method combines the modified penalty and the lagrangian methods 本文提出并分析一种解决不等式约束最优化问题的修改的罚函数法，这一方法综合利用修改的罚函数和拉格朗日法。
The continuity condition of displacements at the interface of elements is enforced by penalty function , of which the penalty number has geometrical meaning and can be determined according to the accuracy desired 单元之间位移场的连续性要求是用罚函数来实现的，其中的罚数具有明确的几何意义，并可按对解的精度要求预先估计出大小。
We analyze such methods in detail and designed a new penalty function , experiment result proved that the genetic algorithm used such penalty function can get better quality of the solution in solving nonlinear programming problems 在这里我们还提出了一种新的罚函数。将运用这种罚函数的遗传算法用于优化非线性约束函数，能够有效的提高解的质量。
The multi - objective decision problem was transformed to the mono - objective problem by the multiply - divide method , and its constraint functions were transformed to the objective functions by a multiplication penalty function 使用化多为一的乘除法，将该多目标决策问题转化为单目标问题求解，提出了使用乘法形式的罚函数将模型中的约束函数转化为目标函数。
In section 4 , a type of multiple - objective fractional bilevel programming problem is introduced , which only the follower ' s function is multiple - objective , an exact penalty function formulation for such a problem is also proposed 第四节研究了一类外层为分式单目标，内层为线性多目标的多目标分式双层规划问题，也给出了它的一个恰当罚函数，推广了前两节的结果。
It can speed the local rate of convergence and improve the accuracy of solution , and to solve nonlinear constraint optimization problems , coa was combined with exact non - differentiable penalty function 它利用混沌变量的特定内在随机性和遍历性跳出局部最优点，并在局部搜索空间经过线性搜索提高解的搜索速度和精度，通过结合精确不可微罚函数以用于求解非线性约束优化问题。
It is based on mpf , which treats inequality constraints with a modified penalty term . the mpf method alternatively minimizes the mpf and updates the lagrange multipliers . the mpf method avoids the in - differentiability of the max { x , 0 } 修改的罚函数法所用的罚函数消除了经典罚函数的主要缺点，修改的罚函数存在解，且在解的邻域内保持目标函数和约束函数的光滑性。
Analyzing the principle of equation fetching something for the coal stacker and establishing mathematics model for it , i analyze the principle of mixing coal while stacking coal elementarily , and use the punish function method to make process optimum 分析了斗轮机等量取料的原理并建立了相应的数学模型，并初步分析了斗轮机在堆煤时的混配煤原理，用罚函数法对其进行了优化。
The thesis deals with a certain fractional bilevel programming problem ( fbp ) . it concerns several particular different programming problems . necessary and sufficient conditions are presented for these problems to admit an exact penalty function formulation 本文研究一类分式双层规划问题( fbp ) ，分情况讨论了几种特殊分式双层规划问题的性质和某类恰当罚函数存在的充分必要条件。
In fegm , the shape function is constructed by the moving least square ( mls ) approximation , the weak form of the equivalent integral equation to the governing equation is employed and essential boundary conditions are imposed by the penalty function method 它采用移动最小二乘法构造形函数，利用能量泛函的弱变分形式的积分方程，并用罚函数法施加本质边界条件，从而得到积分方程的数值解。
