An Implicit Formulation of Mathematical Program with Complementarity Constraints for Application to Robust Structural Optimization

This paper discusses an implicit reformulation of a class of MPEC (mathematical program with equilibrium constraints) problems. We particularly focus on an MPEC problem arising from the robust optimization of elastic structures subjected to the uncertain external load. We first review the relation between the worst-case detection and robust constraint satisfaction of the structural responses, and then derive an MPEC formulation of the robust structural optimization. Since a standard constraint qualification is not satisfied at any feasible solution of an MPEC problem, we propose a reformulation based on the smoothed Fischer–Burmeister function, in which the smoothing parameter is treated as an independent variable. Numerical examples of robust structural optimization are presented to demonstrate that the presented formulation can be solved by using a standard nonlinear programming approach.