论文标题
二次约束的级别集合及其与非convex二次优化问题的关系
Arrangement of level sets of quadratic constraints and its relation to nonconvex quadratic optimization problems
论文作者
论文摘要
我们研究一系列特殊的非凸二次程序，当约束函数的级别集为{\ it it}时，{\ it iT}的排列{\ it iT}时。}在本文中显示，这种类别的问题在不假定priper primal primal primal或dual dial dial prim prater条件下，该类别的问题承认，这类问题是在本类中显示出强大的双重性。我们的结果涵盖了Ye和Zhang在2003年的发展以及广义的信任区子问题（GTRS）作为特殊情况。通过新颖的几何视图和一些简单的示例，我们可以解释为什么当约束的水平设置确实被安排时，问题变得非常困难。
We study a special class of non-convex quadratic programs subject to two (possibly indefinite) quadratic constraints when the level sets of the constraint functions are {\it not} arranged {\it alternatively.} It is shown in the paper that this class of problems admit strong duality following a tight SDP relaxation, without assuming primal or dual Slater conditions. Our results cover Ye and Zhang's development in 2003 and the generalized trust region subproblems (GTRS) as special cases. Through the novel geometric view and some simple examples, we can explain why the problem becomes very hard when the level sets of the constraints are indeed arranged alternatively.
