| Abstract: |
| In this talk we deal with optimization problems in Banach spaces which represent a standard abstract model for many PDE constrained optimization problems. By conical regularization we understand those methods which
construct a family of approximate problems by replacing the constraint cone by an approximating family of cones. These methods are specially indicated for those problems where KKT conditions are not available or such that the
associated multipliers exhibit low regularity. In [A.A. Khan, M. Sama, A new conical regularization for some optimization and optimal control problems: Convergence analysis and finite element discretization, Numer. Funct. Anal. Optim. 34(8), 861-895 (2013)] a set-valued model was proposed in order to prove the convergence in norm of the regularized solutions to the solution of the original problem. In this talk we review some new results on the
differentiability and continuity of the parameter-to-solution map. |
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