摘要
利用非凸优化问题中的Lagrange对偶性思想 ,对可行集进行恰当的细划 ,证明了求解相应的Lagrangian对偶问题所获得的剖分对偶界在适当的假设条件下收敛到原问题的最优值 .应用包括反凸约束凹极小问题以及多胞形上极大仿射比和问题的求解算法 .
The nonconvex global optimization problems are methodic al ly similar to the partial convex optimization problems,which had been studied by the author.We used the Lagrange duality of nonconvex optimization problems and made suitable refined partitioning for the feasible set.It is shown that,under m ild hypotheses ,the partitoning duality bounds obtained by solving corresponding Lagrangian dual converge to the primary problem's optimal value.Applications co mprise all branch-and-bound algorithms for global optimization of nonconvex ob jective functions over polytopes as well as concave minimization under reverse c onvex constraints,and optimization of sums of ratios affine functions over polyt opes.
出处
《三峡大学学报（自然科学版）》
CAS
2001年第5期463-467,共5页
Journal of China Three Gorges University：Natural Sciences
