Ill-posed problems in structural optimization and their practical consequences

Structural optimization problems may be ill-posed or weakly conditioned. Different causes of such ill-conditioning are investigated, which can arise, for example, from the problem statement itself and its probable strong nonconvexity, or the interaction of the optimization algorithm with the discretized physical model. These effects could cause undesirable or incorrect solutions or no meaningful solutions at all. Thus ill-posed or ill-conditioned problems must be treated and assessed carefully. Some approaches to dealing with such problems and possible consequences for the optimal designs are discussed.