基于增广Lagrange函数的等式约束优化算法  

An algorithm based on the augmented Lagrange for equality constrained optimization

作　　者：赵富强[1] 曾玲[1] 王晨[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2007年第3期236-238,共3页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(10501009)

摘　　要：等式约束优化问题是一类比较常见的也是比较简单的约束优化问题,通过研究带有等式约束的优化问题,提出了一个基于增广Lagrange函数的新算法。在新算法中将增广Lagrange函数作为价值函数,将约束优化问题转化为无约束优化问题,用无约束优化方法去解决等式约束优化问题。算法中每一步迭代只需求解一个简单的线性方程组,不需要太大的计算量就可以找到下降方向。算法中初始点是任意的,在适当条件下保证避免罚因子趋于无穷,可以证明算法全局收敛于原问题的KKT点。Equality constrained optimization is the common and easy constrained optimization. A new algorithm based on the augmented Lagrange is proposed by studying equality constrained optimization problems. In the new algorithm, we employ the augmented Lagrange as a merit function and change equality constrained optimization into non-constrained optimization. It can be solved by non-constrained optimization methods. In each iteration the descent direction can be obtained by only calculating a linear system. The initial point is at random. Under suitable conditions, the penalty parameter tends to finite and the algorithm is proved to be globally convergent.

关 键 词：等式约束优化 算法 增广Larange函数 全局收敛 

分 类 号：O221.2[理学—运筹学与控制论]