关键词: 凸n边形面积 全局最优化问题 非线性规划 半机械化方法

Abstract:

This paper aims at proving the validity of an inequality conjecture about convex n-gon when n = 8 and gaining headway in proving it whenn = 9. This co njecture is generally converted into a global optimization problem which is related to the Heilbronn triangular problem. The bottleneck of solving this  problem is the complexity increasing very quickly with n. In this paper, we intend to establish a new semi-mechanization method for solving it. In our a    lgorithm, to reduce the dimension of freedom we first analyze the properties of the optimal configurations and try to obtain the strict polynomial inequ   ality and equation conditions as many as possible. After the precondition process, the mechanization method can be implemented to solve this nonlinear o     ptimization problem, so we call the overall approach as semi-mechanization. Our algorithm will be useful for proving the conjecture with a larger value   of n.

Key words: convex n-gon;global optimization;nonlinear planning, semi-mechanization method