一类带有一个反凸约束全局规划的收敛算法

A CONVERGENT ALGORITHM FOR A CLASS OF GLOBAL OPTIMIZATION WITH A REVERSE CONVEX CONSTRAINT

讨论一类带有一个反凸约束的全局规划（Ｐ）：ｇｌｏｂａｌｍｉｎｆ（ｘ）＝ＣＴｘ，ｓ．ｔ．ｘ∈Ｄ＝｛ｘ｜ｈ（ｘ）≤０｝和ｇ（ｘ）≥ｏ，其中Ｃ≤Ｒｎ，ｇ（ｘ），ｈ（ｘ）是Ｒｎ上的有限凸函数。我们给出这类问题的一个外切型算法。在不需要稳定性假定的一般意义下，证明了算法有限终止于（Ｐ）的全局解，或者算法产生一个收敛到全局解的点列。

In this paper, we are concerned with a class of global optimization problem (P) with a reverse convex constraint:global minf(x)=CTx, subject to x∈D={x|h(x)≤0}, g(x)≥0where C∈Rn, g(x),h (x) are convex finite functions on Rn. An outer cutting algorithm is presented,and under the general meanings, without the stability hypothesis[4], we prove that the algorithm either terminates at after finite steps or converges to the global optimal solution of the problem.