改进Rosenbrock算法求包含平面多边形的最小圆

针对求包含平面多边形的最小圆问题,提出应用Rosenbrock算法求包含平面多边形的最小圆。指出对于上述求最小圆问题,Rosenbrock算法搜索极值点的成败与算法初始点的选择有关。分析了当Rosenbrock算法搜索失败时,目标函数在初始点附近取值情况;对Rosenbrock算法进行了改进：若算法在初始点X0沿初始标准正交向量组的搜索没有取得进展,将初始标准正交向量组作一旋转,得到新的标准正交向量组,算法在初始点X0沿新的标准正交向量组继续搜索。仿真实验表明,改进Rosenbrock算法有更好的搜索效果。

IMPROVING ROSENBROCK ALGORITHM TO FIND THE SMALLEST CIRCLE CONTAINING A POLYGON

The problem of finding the smallest circle that contains a given plane polygon comes from the research fields of machine hardware machining and computer graphics. A method applying Rosenbrock algorithm to find the smallest circle that contains a given plane polygon is put forward in this paper. For the smallest circle problem, the success or failure of searching extreme point by Rosenbrock algorithm depends on the choice of the initial point. This paper analyses the goal function condition near the initial point at which Rosenbroek algorithm failed to search the extreme point, and puts forward an improvement to Rosenbrock algorithm. That is to say, if searches by Rosenbrock algorithm along the directions of the initial standard orthogonal vectors at the initial point X0 have no progress, let＇s rotate the initial standard orthogonal vectors to get new standard orthogonal vectors, and continue searching along the new standard orthogonal vectors at the initial point. Simulation experimental results verify that the improved Rosenbrock algorithm has better search effects.