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A new method for solving structural optimization problems using a local function approximation algorithm is proposed. This new algorithm, called the Generalized Convex Approximation (GCA), uses the design sensitivity information from the current and previous design points to generate a sequence of convex, separable subproblems. The paper contains the derivation of the parameters associated with the approximation and the formulation of the approximated problem. Numerical results from standard test problems solved using this method are presented. It is observed that this algorithm generates local approximations which lead to faster convergence for structural optimization problems.