The research group is interdisciplinary, connecting three subjects at Åbo Akademi University: Mathematics and Statistics from the Department of Natural Sciences, as well as Process Design and Systems Engineering and Thermal and Flow Engineering from the Department of Chemical Engineering. The research is performed interactively between the research blocks Optimization theory, Systems analysis and Engineering Applications.
Recently, the research in several areas of optimization has experienced a significant growth and the results have made it possible to solve many extremely difficult problems not previously solvable. For example, the progress in nonsmooth and nonconvex optimization has opened up new application areas in biotechnology and material science. Also, advances in semidefinite programming has resulted in new, efficient methods for calculating strong bounds in quadratic assignment problems and new types of evolutionary methods has been developed in order to tackle complex problems in industrial decision-making. Nevertheless, the lack of numerically efficient solvers for several important classes of problems is still evident, requiring ongoing effort in this important research field. The goals are focused on creating efficient algorithms for generally convex mixed-integer nonlinear programming (MINLP), reformulation techniques for nonconvex MINLP and new techniques in semidefinite programming and stochastic optimization.
Generic research in mathematical systems theory is important for the OSE group and systems analysis is fundamental for advancing the research in the field. Due to the complexity of financial, ecological and industrial phenomena, it is often practical and purposeful to use stochastic models and analysis for describing and gaining understanding of such systems. Dynamical systems defined by iteration of functions is also an exciting approach. Moreover, many problems can be studied using convex analysis, especially important when developing mixed-integer nonlinear optimization methods.
The generic method development in the research blocks Optimization theory and Systems Analysis is inspired by a large number of industrial case studies and problems previously considered. Several large-scale optimization problems, for which tailored solution systems and tools have been developed in the group, are today in continuous industrial use for example in the iron- and steelmaking, pulp and paper and food industries.