带非凸二次约束的二次比式和问题的全局优化算法(英文)

An Efficient Algorithm of Global Optimization for Sum of Quadratic Ratios Problem with Nonconvex Quadratic Constraints

对带非凸二次约束的二次比式和问题(P)给出分枝定界算法,首先将问题(P)转化为其等价问题(Q),然后利用线性化技术,建立了(Q)松弛线性规划问题(RLP),通过对(RLP)可行域的细分及求解一系列线性规划问题,不断更新(Q)的上下界,从理论上证明了算法的收敛性,数值实验表明了算法的可行性和有效性.

In this paper a branch and bound approach is proposed for solving sum of quadratic ratios problem with nonconvex quadratic constraints （P）,based on the rectangular partition.Firstly,the problem （P） is converted into an equivalent sum of linear ratios problem with quadratic constrains （Q）.Then,utilizing the linear relaxation technique,a liner relaxation programming problem （RLP） about （Q） is established which is solved and provides a lower bound of the optimal value.The proposed algorithm is convergent to the global minimum through the successive refinement of the feasible region and the solution of a series of the linear programming problems.The numerical experiments show the effectiveness and feasibility of the algorithm.