凸约束二次规划问题求解的一般方法

Application of the canonical dual transformation theory to a convex constrained quadratic programming

将标准对偶变换的思想应用到求解凸约束二次规划问题上,并给出了该问题的完全解的形式.标准对偶变换思想的主旨是将原问题通过标准对偶变换的方法转化为其对偶问题,通过求解其对偶问题得到原问题的最优解.这种方法可使原来复杂的问题简单化,并使得原问题与其对偶问题间的对偶间隙为零且不带有任何扰动.应用这种方法我们还可以很容易的得到一些比较好的结果.

This paper analyzes the application of the canonical dual theory to and the form of solution to quadratic programming problems subjected to convex constrains. It is shown that, by this method, these difficult constrained programming can be solved easily, i.e. the perfect dual formulation with zero duality gaps and without any perturbation. Therefore, some satisfactory resuhs can easily be obtained by this method.