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首页> 外文期刊>Journal of Global Optimization >Conic approximation to nonconvex quadratic programming with convex quadratic constraints
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Conic approximation to nonconvex quadratic programming with convex quadratic constraints

机译：具有凸二次约束的非凸二次规划的圆锥近似

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摘要

In this paper, a conic reformulation and approximation is proposed for solving a nonconvex quadratic programming problem subject to several convex quadratic constraints. The original problem is transformed into a linear conic programming problem, which can be approximated by a sequence of linear conic programming problems over the dual cone of the cone of nonnegative quadratic functions. Since the dual cone of the cone of non-negative quadratic functions has a linear matrix inequality representation, each linear conic programming problem in the sequence can be solved efficiently using the semidefinite programming techniques. In order to speed up the convergence of the approximation sequence and relieve the computational effort in solving the linear conic programming problems, an adaptive scheme is adopted in the proposed algorithm. We prove that the lower bounds generated by the linear conic programming problems converge to the optimal value of the original problem. Several numerical examples are used to illustrate how the algorithm works and the computational results demonstrate the efficiency of the proposed algorithm.
机译：在本文中，提出了一种圆锥重整和逼近的方法来解决受多个凸二次约束约束的非凸二次规划问题。原始问题转化为线性圆锥编程问题，可以通过非负二次函数锥的双圆锥上的一系列线性圆锥编程问题来近似。由于非负二次函数的圆锥的对偶圆锥具有线性矩阵不等式表示，因此可以使用半定编程技术有效地解决序列中的每个线性圆锥编程问题。为了加快逼近序列的收敛速度，减轻求解线性圆锥规划问题的计算量，提出了一种自适应方案。我们证明了线性圆锥规划问题产生的下界收敛到原始问题的最优值。几个数值例子用来说明该算法如何工作，计算结果证明了该算法的有效性。

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