关于无线通信中一类二次约束二次规划问题的混合算法

A Hybrid Algorithm for a Kind of Quadratic Constrained Quadratic Programming in Wireless Communications

在无线通信领域,诸如点对点通信的中继波束成形问题等许多问题可以等价为一个或一系列二次约束二次规划问题的求解。该文考虑一类二次约束二次规划问题,其约束中只有二次项和常数项。利用这类问题的特殊结构,该文设计了可行压缩算法,每步迭代时将凸的可行域缩小为一个内部的椭球。迭代点迭代至可行域的边界附近,该文再运用逐步二次规划算法迭代到问题的KKT点。数值实验表明,与现有的凸规划软件包CVX相比,提出的算法在非常短的时间内得到几乎一致的结果。

In wireless communication field, many problems, such as the relay beamforming problem in peer-to-peer communication models, are easily transformed into a serials of quadratic constrained quadratic programming（QCQP） problems. This paper considers a kind of QCQP problems, where there are only quadratic terms and constants in the constraints. A feasible shrinkage method is proposed, where the convex feasible region is compressed as an inner ellipsoid in each iteration. When the iterative point is very close to the boundary of the feasible region, the algorithm switches to the sequential quadratic programming method, and continue the iteration to achieve the KKT point. Simulation results illustrate that our proposed hybrid algorithm achieves almost the same result as the software CVX, with much less computation time.