D．C．集(凸集的差)约束的非凸二次规划的最优解集

The Optimal Solution Set of Non-convex Quadratic Minimization Problem over a D.C.Set

本文研究D.C.集(凸集的差)上极小化非凸二次规划问题的最优解。我们首先证明了该问题的Lagrange对偶的稳定性,即不存在对偶间隙;接着利用该性质得到问题的全局最优性条件和最优解集,它可以像凸规划那样,借助它的对偶问题的解集精确地描述出来。最后,通过一个例子来说明这些结论。

We study the characterization problem of optimal solution sets of non-convex quadratic minimization problems over D.C. set （difference of convex sets）. Firstly, we show that there is no dual gap between the primal problem and its dual problem, and then obtain its globally optimality conditions and optimal solution sets. As a convex programming, we can exactly describe the optimal solution set of the primal problem with the help of the optimal solution set of its dual problem. Finally, we give an example to illustrate the obtained results.