中文摘要：

本文讨论了一类单调非凸约束最优规划的目标函数和约束集的结构特征性质.阐明了如何将所考虑的问题等价地转化为一个递增函数在另一个递增函数水平集上的极大优化问题.在此基础上提出了一个我们称之为修正的新型分枝定界算法.新算法的修正之处是在计算新的极点时,采用了一个有效的新的区域删除模式以构造越来越小的Polyblock集覆盖EnH且不含y,以排除问题（P）可行域中不存在全局ε-最优解的部分.最后,证明了算法的收敛性.初步的数值实验表明算法是有效可行的,可应用于求解更广的一类非凸最优规划.

英文摘要：

In this paper, we investigate some basic properties of the objective function and the constraint set of a class of optimization programs with an additional monotonic non-convex constraint. It is introduced how to convert the original probiem into a new optimization problem,i, e. ,maximizing an increasing funtion over the level set of another increasing function. A new modification branch-and-bound algorithm is developed on the basis of devising efficient solution strategies. The major improvement of the proposed algorithm is that it can construct a smaller polyblock by using a new region-deleting principles. The polyblock still covers E ∩ H but excluding y ,and deletes the subregion without containing the ε-optimal solutions of the problem （P）. Finally,the convergence of the algorithm is proofed. Computation results indicate that the algorithm is not only feasible but also effective. It can be used to solve a broad class of non-convex optimization programs.