无罚函数无滤子的非单调无二次规划方法

Nonmonoton QP free Method Without Penalty Function and Filter

摘要:

提出了求解光滑不等式约束最优化问题的非单调无罚函数无滤子的无二次规划非可行域方法. 通过乘子和非线性互补函数,构造一个等价于原约束问题1阶最优条件的非光滑方程组. 在此基础上,通过牛顿 拟牛顿迭代得到满足1阶最优条件的解,在迭代中采用了无罚函数无滤子的非单调线搜索方法以避免罚函数的选取和滤子的存储,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,试探步更易于接受. 算法不要求迭代点和初始点严格可行. 该算法是可实现的,具有全局收敛性.另外,在较弱条件下可以证明该方法具有超线性收敛性.

Abstract:

We propose a nonmonotone guadratic programming free(QP free) infeasible method without using a penalty function and a filter for inequality constrained nonlinear optimization problems. This iterative method is based on the solution of nonsmooth equations obtained by the multipliers and the nonlinear complementarity problem(NCP) function for the Karush Kuhn Tucker(KKT) first order optimality conditions. Locally, each iteration of this method can be viewed as a perturbation of the mixed Newton quasi Newton iteration on both primal and dual variables for the solution of KKT optimality conditions. We do not use a penalty function and a filter on nonmonotone line searches to avoid the estimation of the penalty parameter and the storage of the filter. The step size is selected so that either the value of the objective function or the measure of the constraint violations is sufficiently nonmonotone reduced. The trial step is more flexibly accepted. It does not demand the strict feasibility of the iterations including the initial point. This method is implementable and globally convergent. Without the second order correction we prove that the method has superlinear convergence rate.