IMPROVED 2-POINT FUNCTION APPROXIMATIONS FOR DESIGN OPTIMIZATION

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 a second 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.