【摘要】 将信赖域与线搜索方法相结合,采用非单调技术,提出一种求解无约束优问题的非单调信赖域算法,并在适当的条件下,证明算法有全局收敛性和Q-二次收敛性.算法在试探步不被接受时,采用非单调线搜索寻找下一迭代点.算法克服了传统非单调算法中用于产生非单调性的参考函数值远大于实际函数值的问题.初步的数值试验证实算法是有效的.更多还原

【Abstract】 Combining trust region and line search with nonmonotone technique,we give a nonmonotone trust region method for unconstrained optimization.Under suitable conditions,the global convergence and Q-quadratic convergence of our algorithm are well proved.When the trial step is not accepted,we get the next iterative point by nonmonotone line search technique.Unlike traditional nonmonotone algorithms,our method can avoid the possibility that the reference function value used to generate non-monotonicity may be much larger than the real function value.Primary numerical results show that this algorithm is efficient.更多还原