A quadratic approximation for structural topology optimization

In topology optimization, it is customary to use reciprocal-like approximations, which result in monotonically decreasing approximate objective functions. In this paper, we demonstrate that efficient quadratic approximations for topology optimization can also be derived, if the approximate Hessian terms are chosen with care. To demonstrate this, we construct a dual SAO algorithm for topology optimization based on a strictly convex, diagonal quadratic approximation to the objective function. Although the approximation is purely quadratic, it does contain essential elements of reciprocal-like approximations: for self-adjoint problems, our approximation is identical to the quadratic or second-order Taylor series approximation to the exponential approximation. We present both a single-point and a two-point variant of the new quadratic approximation.