非线性规划U-D分解方法及其在神经网络训练中的应用
U-D Factorization-Based Nonlinear Programming Method and its Application in Neural Network Training
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摘要: 提出一种有效的U-D分解DFP和BFGS算法.该算法解决了H阵的正定性问题,保 证了算法的数值稳定性,并大大提高了计算效率.对H阵的计算量分析表明,该算法的计算效 率比普通方法高20%,比普通平方根方法高0.4n(n为H阵维数)倍.神经网络训练的应用 表明,新算法比普通DFP和BFGS方法更有效、更准确.Abstract: To solve convergence rate problems of often used DFP and BFCS methods, the stable construction of inverse Hassian matrix are presented. To get high numerical stability and computational efficiency, U-D factorization-based DFP and BFGS algorithms are developed. In the new methods the positive definiteness of the inverse matrix H is ensured and both the stability and convergence of the algorithm is improved. By using rank-one U-D factorization updates of H, the numerical accuracy and efficiency are increased. Operational counts for computing H show that the efficiency of the new algorithm is increased by 20% and the storages of matrix H is reduced by 50%. Results of several numerical example show that the optimization problems can be solved by using the programming methods presented in this paper and accurate results may be obtained.
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