[en] In this paper, various methods based on convex approximation schemes are discussed, that have demonstrated strong potential for efficient solution of structural optimization problems. First, the convex linearization method (CONLIN) is briefly described, as well as one of its recent generalizations, the method of moving asymptotes (MMA). Both CONLIN and MMA can be interpreted as first order convex approximation methods, that attempt to estimate the curvature of the problem functions on the basis of semi-empirical rules. Attention is next directed toward methods that use diagonal second derivatives in order to provide a sound basis for building up high quality explicit approximations of the behaviour constraints. In particular, it is shown how second order information can be effectively used without demanding a prohibitive computational cost. Various first and second order approaches are compared by applying them to simple problems that have a closed form solution.