@phdthesis{Akindeinde2012,
  author    = {Akindeinde, Saheed Ojo},
  title     = {Numerical Verification of Optimality Conditions in Optimal Control Problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-76065},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {This thesis is devoted to numerical verification of optimality conditions for non-convex optimal control problems. In the first part, we are concerned with a-posteriori verification of sufficient optimality conditions. It is a common knowledge that verification of such conditions for general non-convex PDE-constrained optimization problems is very challenging. We propose a method to verify second-order sufficient conditions for a general class of optimal control problem. If the proposed verification method confirms the fulfillment of the sufficient condition then a-posteriori error estimates can be computed. A special ingredient of our method is an error analysis for the Hessian of the underlying optimization problem. We derive conditions under which positive definiteness of the Hessian of the discrete problem implies positive definiteness of the Hessian of the continuous problem. The results are complemented with numerical experiments. In the second part, we investigate adaptive methods for optimal control problems with finitely many control parameters. We analyze a-posteriori error estimates based on verification of second-order sufficient optimality conditions using the method developed in the first part. Reliability and efficiency of the error estimator are shown. We illustrate through numerical experiments, the use of the estimator in guiding adaptive mesh refinement.},
  subject      = {Optimale Kontrolle},
  language  = {en}
}