Enhanced two-point diagonal quadratic approximation methods for design optimization

Based on two-point diagonal quadratic approximation (referred to as TDQA), developed by Kim et al. [Min-Soo Kim, Jong-Rip Kim, Jae-Young Jeon, Dong-Hoon Choi, Efficient mechanical system optimization using two-point diagonal approximation in the nonlinear intervening variable space, J. KSME 15 (2001) 1257–126], enhanced two-point approximation methods are proposed in this paper. The suggested methods reinforce TDQA with new quadratic correction terms using the concept of TANA-3. These methods overcome the disadvantage of TDQA when the derivatives at two design points have the same sign. In addition, the values and derivatives of the proposed approximation functions are completely equal to those of an original function at the two design points whether the derivatives at those points have the same sign or not. Several examples show the numerical performance and accuracy of the proposed methods compared to previous work, and optimization examples show that these methods can successfully reach the optimum via sequential approximation optimization.