一种基于非均匀惩罚因子的序列无约束最优化外点新算法

增广拉格朗日乘子方法（Augmented Lagrange multiplier method）是拉格朗日乘子方法（Lagrange multiplier method）的推广，它是一种序列无约束的最小化技术，包括内点法和外点法，内点法适用于仅有不等式约束的情形，其主要思想是对违背可行性的约束给予一个惩罚。传统的做法是：对所有约束以相同的罚因子，自适应调整Lagrange乘子。提出了一种非均匀惩罚的自适应更新罚因子的方法，即根据近似解对约束违反的严重程度施行不同惩罚的新方法。算例表明，本方法是有效的。

A new method of sequential unconstrained minimization technique for solving constrained minimization problems based on non-homogenous penalty factors

The Augmented Lagrange Relaxation method is effective and efficient at solving constrained optimization problems, which is the extension of the Lagrange Relaxation method and a sequential unconstrained minimization technique （SUMT）. This method includes two types ： exterior and interior . The interior point method is applied to solve optimization problems with only inequality constraints. The main idea of SUMT is that the amount of penalty is exerted on corresponding constraints deviated from the feasibility. The tradition- al decision is to give same penalty on the different constraints without considering their degrees deviating from feasibility, which decreases the rate of convergence of the algorithm. A new method named Non - homogeneous Penalty Factors proposed in this paper,which exerts different penalty factors on different constraints according to their deviations from feasibility. Testing example shows that the new method is more efficient than the traditional one.