Sparse QCQP via Semismooth Newton Method

发布时间：2026-08-26 作者：浏览次数：

Speaker:	罗自炎	DateTime:	2026年8月29日（周六）上午11:00-12:00
Brief Introduction to Speaker: 罗自炎，北京交通大学		Place:	国交二号楼315会议室
Abstract:Quadratically constrained quadratic programming (QCQP) has long been recognized as a computationally challenging problem, particularly in large-scale or high-dimensional settings where solving it directly becomes intractable. The complexity further escalates when a sparsity constraint is involved, giving rise to the problem of sparse QCQP (SQCQP), which makes conventional solution methods even less effective. Existing approaches for solving SQCQP typically rely on mixed-integer programming formulations, relaxation techniques, or greedy heuristics but often suffer from computational inefficiency and limited accuracy. In this work, we introduce a novel paradigm by designing an efficient algorithm that directly addresses SQCQP. To be more specific, we introduce P-stationarity to establish first- and second-order optimality conditions of the original problem, leading to a system of nonlinear equations whose generalized Jacobian is proven to be nonsingular under mild assumptions. Most im...