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

In this paper, a rational approximation approach with linear functional denominator and numerator at two expanded points is used to obtain a modified Newton method, which converges faster and more stably than the usual Newton method in solving unconstrained optimization problems. To apply this modified Newton method to solve the constrained optimization problem, first, some disadvantages of the dual algorithm for separable variables introduced by Fleury are avoided resulting in an improved dual method. Then a modified dual method based on the rational approximation is proposed to solve the constrained optimization problem. Finally, the improved dual method and the modified dual method are applied to the solution of truss structural optimization problems. The paper shows that the rational approximation method has excellent prospects for applications.