Improved Two-Point Function Approximations for Design Optimization

摘要

Two-point approximations are developed by utilizing both the function and gradient information of two data points. The objective of this work is to build a high-quality approximation to realize computational savings in solving complex optimization and reliability analysis problems. Two developments are proposed in the new two-point approximations: 1) calculation of a correction term by matching with the previous known function value and supplementing it to the first-order approximation for including the effects of higher order terms and 2) development of asecond-order approximation without the actual calculation of second-order derivatives by using an approximate Hessian matrix. Several highly nonlinear functions and structural examples are used for demonstrating the new two-point approximations that improved the accuracy of existing first-order methods.