摘要
In this paper,an adaptive cubic regularisation algorithm based on affine scaling methods(ARCBASM)is proposed for solving nonlinear equality constrained programming with nonnegative constraints on variables.From the optimality conditions of the problem,we introduce appropriate affine matrix and construct an affine scaling ARC subproblem with linearized constraints.Composite step methods and reduced Hessian methods are applied to tackle the linearized constraints.As a result,a standard unconstrained ARC subproblem is deduced and its solution can supply sufficient decrease.The fraction to the boundary rule maintains the strict feasibility(for nonnegative constraints on variables)of every iteration point.Reflection techniques are employed to prevent the iterations from approaching zero too early.Under mild assumptions,global convergence of the algorithm is analysed.Preliminary numerical results are reported.
本文提出一种基于仿射尺度方法的自适应三次正则化算法(ARCBASM),用于求解带有变量非负约束的非线性等式约束规划问题.从问题的最优性条件出发,引入合适的仿射矩阵,构造了具有线性化约束的仿射ARC子问题.采用复合步方法和既约Hessian法处理线性化约束.由此导出了一个标准的无约束ARC子问题,其解可以提供足够的下降量.边界规则保证了每个迭代点的严格可行性(对于变量的非负约束).反射技术被用来防止迭代点过早地接近零.在适当的假设条件下,分析了算法的全局收敛性,并报告了初步的数值结果.
出处
《应用数学》
北大核心
2026年第1期258-277,共20页
Mathematica Applicata
基金
Supported by the National Natural Science Foundation of China(12071133)
Natural Science Foundation of Henan Province(252300421993)
Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110005)。
