论文标题
抛物线放松，用于四次约束二次编程 - 第二部分：理论和计算结果
Parabolic Relaxation for Quadratically-constrained Quadratic Programming -- Part II: Theoretical & Computational Results
论文作者
论文摘要
在这项工作的第一部分[32]中，我们引入了一种凸抛物线松弛，以进行四次约束的二次程序，以及顺序惩罚的抛物线抛物性松弛算法，以恢复近乎最佳的可行解决方案。在第二部分中，我们表明，从可行的解决方案或满足某些规律性条件的几乎可行的解决方案开始，顺序惩罚的抛物线释放算法的融合到满足Karush-Kuhn-tucker优化条件的点。接下来，我们介绍基准非凸QCQ问题的数值实验，以及系统识别问题的大规模实例，证明了所提出的方法的效率。
In the first part of this work [32], we introduce a convex parabolic relaxation for quadratically-constrained quadratic programs, along with a sequential penalized parabolic relaxation algorithm to recover near-optimal feasible solutions. In this second part, we show that starting from a feasible solution or a near-feasible solution satisfying certain regularity conditions, the sequential penalized parabolic relaxation algorithm convergences to a point which satisfies Karush-Kuhn-Tucker optimality conditions. Next, we present numerical experiments on benchmark non-convex QCQP problems as well as large-scale instances of system identification problem demonstrating the efficiency of the proposed approach.
