Approximationstheorie - Fakultät für Mathematik - TU Chemnitz: Department of Mathematics: Approximation Theory: Diploma and Master Themes
Diploma and Master's Thesis Themes
Our working group's research is focused on subjects belonging to Convex Analysis,
Optimization and Approximation Theory
Our primary interests concern theoretical problems and applications
within duality theory for scalar and multiobjective optimization probles.
Moreover, we deal with duality and optimality conditions for optimization problems
involving DC (difference of convex), entropy and fractional functions, generalized convexity,
variational inequalities, regularity conditions (constraint qualifications) for
optimization problems, properties of the conjugate functions and
theorems of the alternative.
Based on a new duality concept developed in our working group, we have
obtained new results within the mentioned fields, which may be found in a series of
talks at conferences and meetings, publications, diploma, Master's and Ph.D theses.
Applied topics are also equally treated. Here belong location, approximation and portfolio optimization problems, as well as third-part projects within Data Mining und Information (Text) Retrieval.
Diploma and Master's thesis themes can be offered to the interested students
within the mentioned areas. You are referred to Professor Wanka or Dr. Boţ
for further information.
Some possible themes follow:
- Classical and new theorems of the alternative based on conjugate duality
- Weak efficiency and duality in multiobjective optimization
- Farkas-type and theorems of the alternative based on duality for composed functions
- Comparisons between different duality concepts for multiobjective optimization problems
- Notions of Convex Analysis for vector-valued and set-valued functions and mappings
- Notions of discrete Convex Analysis and duality
- Overview, comparisons and unification of actual research in duality within location problems
- Duality and optimiality conditions in portfolio optimization
- Investigations on ε-duality and ε-optimality for convex optimization problems
- Benefit and utility functions in mathematical Economics in the light of Convex Analysis
