SIAM Journal on Optimization, Volume 30, Issue 4, Page 2983-2997, January 2020.
A quadratically constrained quadratic program (QCQP) is an optimization problem in which the objective function is a quadratic function and the feasible region is defined by quadratic constraints. Solving nonconvex QCQP to global optimality is a well-known NP-hard problem and a traditional approach is to use convex relaxations and branch-and-bound algorithms. This paper makes a contribution in this direction by showing that the exact convex hull of a general quadratic equation intersected with any bounded polyhedron is second-order cone representable. We present a simple constructive proof and some preliminary applications of this result.

中文翻译：

---

多边形上二次约束的凸包

SIAM优化杂志，第30卷，第4期，第2983-2997页，2020年1月
。二次约束二次规划（QCQP）是一个优化问题，其中目标函数是二次函数，而可行区域由二次约束定义。将非凸QCQP求解为全局最优是一个众所周知的NP难题，而传统方法是使用凸松弛和分支定界算法。通过证明与任何有界多面体相交的一般二次方程的精确凸包是二阶锥可表示的，本文对此做出了贡献。我们提出了一个简单的建设性证明，并对此结果进行了一些初步的应用。