应用两点有理逼近改进的牛顿法和对偶法

Modified Newton’s method and dual method through rational approximation at two expanded points

应用分子、分母皆线性的两点有理逼近改进了解无约束极值的Ｎｅｗｔｏｎ法，获得了收敛快而稳的计算效果．将此法应用于约束优化问题，克服了Ｆｌｅｕｒｙ将对偶规划引入可分离变量问题求解中的缺陷．提出了采用上述逼近的对偶方法，适用于约束优化问题的求解．将该方法和改进的Ｆｌｅｕｒｙ方法均在桁架结构优化上进行了成功的应用，工作表明，两点有理逼近有很好的应用前景．

A RATP(rational approximation with linear functional denominator and numerator at twoexpanded points) is used to modify Newton-Raphson method. Numerical results demonstratethat the modified N-R method converges faster and stabler than the primary one in solvingunconstrained optimization problem.To apply this modified N-R method to solve const rainedoptimization problem , some drawbacks of separable variables dual algorithm introduced by Fleuryare avoided basically.Then a modified dual method based on RATP is proposed to solveconstrained optimization problem. Finally , the improved Fleury’s dual algorithm and themodified dual method are applied to solve truss structural optimization problem. The work of thepaper shows that RATP will have an excellent prospect of appllcations.