Our research emphasizes mathematical methods of finite dimensional continuous optimization. In such problems an objective function depending on a finite dimensional continuous decision variable is optimized under a finite number of inequality and equality constraints. Applications comprise the following areas:
- Management problems (e.g., cost minimal transportation plans, profit maximization),
- Geometrical problems (e.g., optimal sensor placement, waste minimization),
- Mechanical problems (e.g., truss topology design),
- Chemical problems (e.g., protein folding),
- Statistical problems (e.g., parameter fitting, data classification).
Furthermore, finite dimensional continuous optimization problems arise as subproblems by
- discretization of the infinite dimensional decision variables in optimal control (thereby giving rise to specially structured, e.g. sparse and/or block-structured, Jacobians and Hessians),
- discretization of the infinite index set of constraints in semi-infinite and robust optimization,
- relaxing integrality constraints in integer or mixed-integer optimization problems.
Important extensions of finite dimensional continuous optimization include the cases of
- infiniteley many inequality constraints (semi-infinite optimization),
- partially discrete decision variables (mixed-integer optimization),
- several competing objectives (multi-objective optimization),
- parameter dependent objective and constraint functions (parametric optimization, sensitivity analysis),
- several coupled parametric optimization problems (Nash games).
Bachelor amd master theses as well as dissertations at the chair mainly treat theory, algorithms, and applications from the above areas. Further information, e.g. on central research questions und challenges in continuous optimization, may be found on these slides.