A non-conforming dual approach for adaptive Trust-Region reduced basis approximation of PDE-constrained parameter optimization

In this contribution we propose and rigorously analyze new variants of adaptive Trust-Region methods for parameter optimization with PDE constraints bilateral constraints. The approach employs successively enriched Reduced Basis surrogate models that are constructed during the outer loop used as model function method. Each sub-problem is solved projected BFGS Moreover, a non-conforming dual (NCD) to improve standard RB approximation optimality system. Rigorous improved posteriori error bounds derived prove convergence resulting NCD-corrected algorithm. Numerical experiments demonstrate enables reduce computational demand large scale or multi-scale constrained problems significantly.