The problem of the relaxation of optimal design problems for multiphase composite structures in the presence of constraints on the gradient of the state variable is addressed. A relaxed formulation for the problem is given in the presence of either a finite or infinite number of constraints. The relaxed formulation is used to identify minimizing sequences of configurations of phases.
Publication Source (Journal or Book title)
Journal of Optimization Theory and Applications
Lipton, R. (2002). Relaxation through homogenization for optimal design problems with gradient constraints. Journal of Optimization Theory and Applications, 114 (1), 27-53. https://doi.org/10.1023/A:1015408020092