Professor in Applied Mathematics
Algorithms for large-scale nonlinear and semidefinite optimization
We are interested in the development of algorithms and software for large-scale optimization problems. We aim at combining efficient algorithms of mathematical optimization with powerful tools of numerical linear algebra. Particular interest is given to linear and nonlinear semidefinite programming problems, and problems with special data structures. Professor Kocvara is a co-author of a computer program PENNON which is the first known code that can solve optimization problems with a combination of standard non-linear and matrix inequality constraints. Possibilities for PhD work include, among others, development of novel algorithms using special structure of the underlying models, special data structure of the problems, and strong links to modern techniques of numerical linear algebra, like multigrid and domain decomposition.
Optimization of elastic structures
Our goal is to design optimal material properties and distribution within an elastic body. Emphasis is given to so-called Free Material Design which deals with the question of finding the lightest structure subject to one or more given loads when both the distribution of material and the material itself can be freely varied. The techniques and tools of material and topology optimization accelerated rapidly in the last ten years and recently found a way to many industrial companies, in particular in the automotive and aircraft industry. Prof. Kocvara is a member of the team that developed a computer code MOPED used, among others, in the design of components of the new Airbus A380. Possibilities for PhD work include, among others, development of new mathematical models for topology and material optimization based, in particular, on (nonlinear) semidefinite programming.