Sequential Convex Programming for Structural Optimization Problems

Abstract

In this Lecture, several recent methods based on convex approximation schemes are discussed, that have demonstrated strong potential for efficient solution of structural optimization problems. First, the now well established "Approximation Concepts" approach is briefly recalled for sizing as well as shape optimization problems. Next, the "Convex Linearization" method (CONLIN) is described, as well as one of its recent generalization, the "Method of Moving Asymptotes" (MMA). Both CONLIN and MMA can be interpreted as first order convex approximation methods, that attempt to estimate nonlinearity 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 a prohibitive computational cost. Various first and second order approaches have been successfully tested on simple problems that can be solved in closed form, on sizing optimization of trusses, and on two-dimensional shape optimal design problems. In most cases convergence is achieved within five to ten structural reanalyses.