A smoothing scheme for a minimum weight problem in structural plasticity

We revisit an important and challenging class of minimum weight structural plasticity problems, the feature of which is the presence of complementarit y constraints. Such relations mathematically express the perpendicularity o f two sign-constrained vectors and mechanically describe an inherent proper ty of plasticity. The optimization problem in point is referred to in the m athematical programming literature as a Mathematical Program with Equilibri um Constraints (MPEC). Due to its intrinsic complexity, MPECs are computati onally very hard to solve. In this paper, we adopt recent ideas, proposed b y mathematical programmers, on smoothing to develop a simple scheme for ref ormulating and solving our minimum weight problem as a standard nonlinear p rogram. Simple examples concerning truss-like structures are also presented for illustrative purposes.