Sparse QCQP via Semismooth Newton Method
来源：
发布时间：2026-08-26
报告时间：- 2026年8月29日（周六）上午11:00-12:00
- 报告地点：
- 国交二号楼315会议室
- 报告人：
- 罗自炎
- 报告人单位：
- 北京交通大学
- 邀请人：
- 张雄军
- 摘要：
- 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 importantly, these equations facilitate the development of a semismooth Newton-type method that exhibits significantly low computational complexity due to the sparsity constraint, achieves a locally quadratic convergence rate, and performs well on largescale instances in numerical experiments. This is a joint work with Shuai Li and Shenglong Zhou.
罗自炎（北京交通大学）
