不等式约束二次规划的不动点迭代

Fixed Iterative Method for Solving the Inequality Constrained Quadratic Programming Problem

提出了不等式约束二次规划问题的一个光滑型方法。通过分析最优解满足一线性互补问题这一特征,利用信息论中的极大熵原理求解并获得了基于不动点的光滑迭代算法。分析了解存在的必要条件及迭代算法收敛性,给出了算法的迭代格式,通过数值模拟证明该算法的有效性,从而为不等式约束二次规划问题的求解提供了新途径。

With respect to inequality constrained quadratic programming, a smooth method is presented to analyze the optical solution and to convert condition to linear complementary problem （LCP）. And then we apply the entropy function to solve LCP, the fixed iterative method is obtained. An iterative projection is given and a necessary condition is proposed. The numerical results show that the algorithm is effective, and the new method is offered for inequality constrained quadratic programming.