It is well known that a quadratic programming minimization problem with one negative eigenvalue is NP-hard. However, in practice one may expect such problems being not so difficult to solve. We suggest to make a single partition of the feasible set in a concave variable only so that a convex approximation of the objective function upon every partition set has an acceptable error. Minimizing convex approximations on partition sets provides an approximate solution of the nonconvex quadratic program that we consider. These minimization problems are to be solved concurrently by parallel computing. An estimation of the number of partition sets is given. The study presents a computational comparison with a standard branch-and-bound procedure.

众所周知，具有一个负特征值的二次规划最小化问题是NP难的。但是，在实践中，人们可能会希望解决这些问题并不是那么困难。我们建议仅在凹变量中对可行集进行单个划分，以使目标函数在每个划分集上的凸近似都具有可接受的误差。最小化分区集上的凸近似值提供了我们考虑的非凸二次程序的近似解。这些最小化问题将通过并行计算同时解决。给出了分区集数量的估计。该研究提出了与标准分支定界程序的计算比较。