TU CE GSC CE People at the Graduate School CE Principal Investigators Winnifried Wollner - Mathematical Optimization

The research group is concerned with the discrete approximation to infinite dimensional optimization problems, typically involving differential operators in partial differential equations (PDE) or corresponding variational inequalities (VI). Of immense interest are problems where additional constraints need to be imposed on the solutions of the PDE or VI. Such problems arise in many fields, e.g., in the optimal cooling of steel or glass, the design of optimal structures, or the identification of parameters in models to match given observations.

Within this research area, the group analyzes optimization algorithms, partly well known in the finite dimensional setting, to evaluate the applicability in the approximation of infinite dimensional problems; and to propose appropriate modifications to these algorithms should they turn out to give trouble in solving the infinite dimensional problem, and in particular the large-scale discrete approximations. Moreover the group is concerned with a priori error analysis to judge the error between some discrete approximation and the infinite dimensional limit to be able to assert a certain increase in approximation accuracy within the computable discrete approximations. Finally, novel a posteriori error estimates are developed to allow for more efficient adaptive discretizations and an effective balancing between discretization error and inaccurate solution of the discrete minimization problems with respect to certain goal quantities, that are of interest in the given computation.

Technische Universität Darmstadt

Graduate School CE

Dolivostraße 15

D-64293 Darmstadt

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Office | S4|10-322 |

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