A system, method, and software product for an accelerated design optimization is described. Engineers/designers/users define an initial design with a set of responses and constraints on the responses in a design optimization process. A plurality of approximations to the responses around the initial design is created to represent an engineering design space. A current optimal design is determined from the approximations subject to the set of constraints. Actual structural response of the current optimal design is calculated. As a result, the residual between the actual response and the approximated response can be established. When the optimization process has not reached convergence, another set of approximations is created around the current optimal design. Instead of using the original set of constraints, the new set of constraints is adjusted with the calculated residual, so that the design optimization process can achieve convergence much faster.