i am performing parameter identification for a non-linear partial differential equation (elasticity) that I solve with finite elements.
My optimization problem is a non-linear least squares data-fitting problem because I want to fit the parameters to measured data, e.g. coming from Digital-Image-Correlation. The residual vector within the optimization is the solution vector (or a subset of it) of the discretized PDE.
At the moment, I use open-source software (MATLAB) to solve the optimization problem, but I feel I have to get more background about optimization in the context of finite element model updating. I rely on interior-point and trust-region methods to solve the optim problem.
For finite elements, I know typical reference books that are common in this field, but for optimization, I do not know many yet. I found books like "Numerical Optimization from Nocedal and Wright", but I do not have the expertice to assess whether this is a common book in numerical optimization or not.
I thought it is useful to reach out to the community with this question since it maybe also helps other people in the future.