Abstract: In this paper an interior penalty function method is applied to minimize the weight of a wing structure under the constraints of flutter, strength and minimum gage. Three unconstrained optimization methods'steepest descent method, DFP variable metric algorithm and BFGS variable metric algorithm, are compared with each other. The quadratic interpolation method with the constraints approximated by quadratic polynomials is used in the one-dimensional search. Respective convergent criterions used in the interior penalty function are presented. Several ways to reduce computer time are pointed out and discussed here.