一类扩展的CDT问题存在对偶间隙的充要条件

Research on a Second-order Cone Reformulating Problem of CDT Problem

在这篇文章中,作者研究一类带有两个二次约束的CDT问题,其中一个是单位球约束,一个是椭球约束。选取合适的通过最优线段的超平面,在不分割可行域的情况下,通过二阶锥重塑技术和半正定松弛的方法,得到了该CDT问题的二阶锥重塑问题存在对偶间隙的充要条件,并给出了理论证明,为以后缩小甚至消除CDT问题的对偶间隙做铺垫。

In this paper, the author study a class of CDT problem with two quadratic constraints, one of which is the unit ball constraint and the other is the ellipsoid constraint. Try to find the appropriate hyperplane through the optimal line segment without dividing the feasible region. By using the second-order cone recombination technique and the SDP relaxation method, the necessary and sufficient conditions for the existence of the dual gap in the second- order cone reformulating problem of the CDT problem are obtained, and the theoretical proof is given which is paved to reduce or even eliminate the dual gap of the CDT problem.