Plugging the representation (3.52c) in (3.47), we establish the following equivalence.
Proposition 3.8. The topology optimization problem (3.48) can be equivalently stated with respect to the primal and dual state variables. Find (ω*, ε*, x*) ∈ such that
Further we provide asymptotic analysis of the objective as ε ↘ +0.
As ε = 0, problem (3.51 ...