Computational issues in optimization-based design

In this paper we consider certain features of optimization-based design, wherein the physical laws, expressed as boundary value problems, are incorporated as constraints. One such idea is a modification of the optimization algorithm to include a linearized constraint which effectively reduces the dimensionality. A second approach exploits domain decomposition ideas to analyze the physics on separate domains with compatibility being enforced by the optimization algorithm. Both cases suggest computational approaches that provide significant savings over methods that do not exploit problem structure.