桂胜华等曾提出含弱互补函数的不等式约束最优化问题的拉格朗日一牛顿法和拟牛顿法,但算法中计算Hesse矩阵的工作量较大,且该算法仅能解不等式约束最优化问题.论文改进了桂胜华等的算法,用拟牛顿公式代替了Hesse矩阵,并把解不等式约束最优化问题推广到既含不等式约束又含等式约束最优化问题;证明了此算法具有全局收敛性和局部超线性收敛性.
In the paper of Gui Sheng - hua et al, a Lagrange-Newton Method with the slack NCP function was proposed for constraint optimization. In this paper, propose a new Lagrange-Quasi-Newton method with the slack NCP function for inequality constraint optimization. Use the Quasi-Newton method instead of the Hessian matrix in the new method. The method is globally convergent and superlinear convergence rate.