A new two-point approximation approach for structural optimization

The objective of this work is to build up a high-quality approximation scheme to realize computational savings for the solution of structural optimization problems. To this end, a newly developed two-point approximation scheme is proposed. This scheme is constructed by the linear combination of Taylor expansions in terms of both original and reciprocal variables. The coefficients of the combination are determined by utilizing both the function and gradient information of two different design points obtained during the process of optimization. Based on this approach, the accuracy of the existing constraint approximation methods can be improved. The effectiveness of the proposed approach is demonstrated on a number of numerical examples. The numerical results are also compared with those of previously published work.