等式约束优化一个新的SQP算法  

A new SQP algorithm for equality constrained optimization

作　　者：赵富强[1] 曾玲[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：《纯粹数学与应用数学》2009年第2期276-283,共8页Pure and Applied Mathematics

基　　金：国家自然科学基金(10501009);广西自然科学基金(0728206)

摘　　要：提出了一个处理等式约束优化问题新的SQP算法,该算法通过求解一个增广Lagrange函数的拟Newton方法推导出一个等式约束二次规划子问题,从而获得下降方向.罚因子具有自动调节性,并能避免趋于无穷.为克服Maratos效应采用增广Lagrange函数作为效益函数并结合二阶步校正方法.在适当的条件下,证明算法是全局收敛的,并且具有超线性收敛速度.In this paper, a new SQP method is presented to solve equality constrained optimization. It obtains descent direction by solving a equality constrained optimization subproblem which is deduced by solving the augmented Lagrangian in quasi-Newton method. The penalty parameter is adjusted automatically and avoided tending to infinity. In order to conquer Maratos effect, it takes augmented Lagrangian as a merit function and combines two-step revised method. Under some suitable assumptions, we prove that the algorithm is global convergence as well as superlinear convergence.

关 键 词：等式约束优化 SQP算法 等式约束二次规划 全局收敛 超线性收敛 

分 类 号：O221.2[理学—运筹学与控制论]