【摘要】 非线性最优化算法主要包括两个步骤:一是利用目标函数和约束函数的导数或相关信息来确定搜索方向,二是利用一维搜索和信赖域方法来确定沿搜索方向步长.一维直线搜索在各种教科书及参考文献中被广泛地讨论过,而另一种搜索方法弧搜索方法,在某些情况下更有效却鲜为人知.本文讨论弧搜索方法的一些细节及在各种最优化问题中的应用,并指出弧搜索技术比直线搜索对某些问题更具优越性.更多还原

【Abstract】 Line search and trust region are two most popular techniques to generate steps with the help of derivatives of the objective and constraint functions.However,there is a lessknown technique,arc-search method,which is relatively new and may generate more efficient algorithms in some cases.In this paper,we will survey this technique,discuss its applications in different optimization problems,and explain its potential improvements over traditional line search method.更多还原