带一般约束无导数优化问题的改进信赖域算法

摘要

通过建立约束违和函数,利用进步栏阈法(PB 策略)筛选出插值点集中性质较好的迭代点,同时修正子问题的初始增广Lagrange乘子,提出一种改进的无导数信赖域(TRDF)算法,并证明了改进算法的收敛性.针对不同维数测试问题的数值试验结果表明,改进算法有效降低了求解二次插值模型的迭代次数和迭代时间.%We presented an improved trust-region derivative-free (TRDF)algorithm.In the proposed method,we established the constraint violation function,chose a better iteration point by using the progressive barrier (PB)strategy modified sub problem of the initial augmented Lagrangian multiplier,and proved the convergence of the improved algorithm.Numerical experiments for different dimensions of the test results show that the improved algorithm effectively reduces the number of iterations and the iteration time for solving polynomial interpolation model.