一个新的求解非线性等式约束的QP-free非可行域方法  

A New QP-free Infeasible Method for Nonlinear Equality Constrained Problems

作　　者：刘爱兰[1,2] 

机构地区：[1]同济大学数学系,上海200092 [2]上海电力学院数理学院,上海200090

出　　处：《上海电力学院学报》2014年第2期193-197,共5页Journal of Shanghai University of Electric Power

基　　金：国家自然科学基金资助项目(11371281;10771162)

摘　　要：提出了一个求解非线性等式约束优化问题的无罚函数无滤子的非单调QP-free非可行域方法.利用乘子和原始变量,构造一个等价于原约束问题一阶最优KKT条件的方程组.通过牛顿-拟牛顿迭代得到满足一阶KKT条件的解.采用了非单调的无罚函数无滤子线搜索方法,每次迭代使得目标函数或者约束违反度函数具有充分的非单调下降,可以取得更好的试探步长.该算法具有全局收敛性,在较弱条件下可以证明该方法具有超线性收敛性.A nonmonotone QP-free infeasible method is proposed without using a penalty function and a filter for nonlinear equality constrained optimization problems. This iterative method is based on the solution of equations which are obtained by the multipliers and the primal variables for the KKT first-order optimality conditions. Either the value of the objective function or the measure of the constraint violations is sufficiently nonmonotone reduced. It does not demand the strict feasibility of the iterations including the initial point. This method is globally convergent. Under mild conditions it is proved that the method has superlinear convergence rate.

关 键 词：非单调 等式约束 QP—free非可行域方法 收敛性 

分 类 号：O221.2[理学—运筹学与控制论]