For a large scaled optimization based on response surface methods, an effic
ient quadratic approximation method is presented in the context of the trus
t region model management strategy. If the number of design variables is n,
the proposed method requires only 2n + 1 design points for one approximati
on, which are a center point and two additional axial points within a syste
matically adjusted trust region. These design points are used to uniquely d
etermine the main effect terms such as the linear and quadratic regression
coefficients. A quasi-Newton formula then uses these linear and quadratic c
oefficients to progressively update the two-factor interaction effect terms
as the sequential approximate optimization progresses. In order to show th
e numerical performance of the proposed method, a typical unconstrained opt
imization problem and two dynamic response optimization problems with multi
ple objective are solved. Finally, their optimization results compared with
those of the central composite designs (CCD) or the over-determined D-opti
mality criterion show that the proposed method gives more efficient results
than others.