求解无约束优化问题的多维滤子信赖域方法

A Multidimensional Filter Trust Region Method for Unconstrained Optimization

无约束优化问题广泛存在于工程、科学计算等领域.本文提出了修正的多维滤子信赖域算法,将信赖域子问题中柯西步的求解独立出来,一旦发现二次模型非凸,便直接采用柯西点作为下一步迭代点.新算法无需考虑迭代产生的非凸点,编程以及全局收敛性的证明过程较为简洁.最终,数值计算结果表明算法的可行性和有效性.

Unconstrained optimization arises in engineering and scientific computing areas.We present a modified filter trust region method.It employs the Cauchy point directly,when the trust region subproblem is nonconvex.Without the consideration of nonconvex points,the algorithm and the global convergence analysis are easier.Numerical results show that the algorithm is efficient and reliable.