A SADDLE-POINT THEOREM WITH APPLICATION TO STRUCTURAL OPTIMIZATION

The relaxation for optimal compliance design is independent of whether the underlying elastic problem is formulated in terms of displacements or strains. For the purposes of numerical experimentation and computation, it may be advantageous to formulate optimal design problems in terms of displacements as is done in Ref. 1. The relaxed problem delivered by the displacement-based formulation is of min-min-max type. Because of this, efficient numerical implementation is hampered by the order of the last two min-max operations. We show here that the last two min-max operations may be exchanged, facilitating an efficient numerical algorithm. We remark that the rigorous results given here corroborate the numerical methods and experiments given in Ref. 1.