%0 Journal Article
%T 基于分式模型的非单调自适应信赖域方法<br>A Nonmonotone Adaptive Trust Region Method Based on Fractional Model
%A 杨玉梅
%J Advances in Applied Mathematics
%P 2207-2219
%@ 2324-8009
%D 2023
%I Hans Publishing
%R 10.12677/AAM.2023.125226
%X 本文针对无约束优化问题提出了一个基于分式模型的非单调自适应信赖域的算法。首先用折线法求解子问题，之后算法结合非单调线搜索技术得到步长，产生下一个迭代点，提高算法的收敛速度；并引入自适应半径，避免传统信赖域半径更新的局限性。在一定的假设条件下，证明了该算法具有全局收敛性，数值实验证明了非单调自适应分式模型信赖域算法是有效的并且优于原来求解分式模型的算法，并且比二次模型和锥模型更为有效和稳健。<br />
This paper proposes a nonmonotone adaptive trust region algorithm based on fractional model for unconstrained optimization problems. First, the dogleg step method is used to solve the sub- problem, and then the algorithm combines nonmonotonic line search technology to obtain the step size, generates the next iteration point, and improves the convergence speed of the algorithm; The adaptive radius is introduced to avoid the limitations of traditional trust region radius updating. Under certain assumptions, it is proved that the algorithm has global convergence. Numerical experiments show that the nonmonotonic adaptive fractional model trust region algorithm is effective and superior to the original algorithm for solving fractional models, and is more effective and robust than the quadratic model and the cone model.
%K 无约束优化，分式模型，非单调信赖域，自适应半径，全局收敛性<br>Unconstrained Optimization
%K Fractional Model
%K Nonmonotone Trust Region
%K Adaptive Radius
%K Global Convergence
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=65582