二次规划问题的一个全局收敛的内点型算法

目标函数是二次函数而约束函数是线性函数的规划问题称为二次规划问题,它是最简单的一类非线性规划问题,利用二次规划问题的约束函数为线性函数的这个特点,结合约束优化问题的一阶最优性条件,提出了二次规划问题的一个全局收敛的内点型算法.算法比较简单,每一步只需要求解一个线性方程组,不需要大量的计算就可以得到可行下降方向,再设置一组参数,沿着该方向进行线性搜索.算法每次迭代都能保持不等式约束函数的严格可行性,具有内点法的特点,而且在不需要凸性的假设下证明了算法是具有全局收敛性的.最后给出了数值实验,进一步证实了算法的可行性与收敛性.

A global convergence inner-point style algorithm for generic quadratic programming problem

The program with quadratic objective function and linear constrained function is Quadratic Programming problem.It is the simplest nonlinear programming.In this paper a new algorithm for quadratic programming is proposed with the characteristic of quadratic programming and the first order conditions of constrained programming employed.This algorithm is simple and in each iteration the feasible search direction can be obtained by only calculating one linear system.The feasible search direction which ensures that iteration belongs to the interior of feasible field of descent and can be obtained by solving a linear system per single iteration and then making a set of parameters for the linear search.Global convergence of the proposed algorithm is proved without any assumptions of convexity.Finally,the testing examples for the algorithm are given.