On Dealing with Minima at the Border of a Simplicial Feasible Area in Simplicial Branch and Bound
研究单纯形分支定界全局优化算法中，如何利用目标函数的单调性来缩小搜索区域，特别是当极小点位于可行域边界时，通过识别单调方向和边界面来简化问题。
Abstract We consider a simplicial branch and bound Global Optimization algorithm, where the search region is a simplex. Apart from using longest edge bisection, a simplicial partition set can be reduced due to monotonicity of the objective function. If there is a direction in which the objective function is monotone over a simplex, depending on whether the facets that may contain the minimum are at the border of the search region, we can remove the simplex completely, or reduce it to some of its border facets. Our research question deals with finding monotone directions and labeling facets of a simplex as border after longest edge bisection and reduction due to monotonicity. Experimental results are shown over a set of global optimization problems where the feasible set is defined as a simplex, and a global minimum point is located at a face of the simplicial feasible area.