Väitös (matematiikka): FL Ville Rinne

FL Ville Rinne esittää väitöskirjansa ”A theory of nonsmooth optimization problems with fuzzy parameters” julkisesti tarkastettavaksi Turun yliopistossa perjantaina 27.11.2026 klo 11.00 (Turun yliopisto, Agora, XX-luentosali, Vesilinnantie 3, Turku).

Vastaväittäjänä toimii professori Montaz Ali (Witwatersrandin yliopisto, Etelä-Afrikka) ja kustoksena tohtori Yury Nikulin (Turun yliopisto). Tilaisuus on englanninkielinen. Väitöksen alana on matematiikka.

Tiivistelmä väitöstutkimuksesta:

Optimization is the study of how to find the best possible solution to a problem. It is used in many areas where we need to make decisions, such as engineering, economics, resource allocation, and planning. However, real-world optimization problems are often more complicated than the mathematical models used to describe them. The functions involved may not be smooth, and the information available may be uncertain or imprecise.

This dissertation develops mathematical methods for optimization problems that involve both of these difficulties. In particular, it studies problems in which the quantities involved can be represented by fuzzy numbers. Fuzzy numbers provide a way of describing information that is not known exactly, such as an estimate that a cost is approximately a certain amount rather than exactly that amount.

The dissertation extends classical optimization theory by using generalized forms of convexity that allow a wider range of problems to be studied. Because the functions considered may not be differentiable, generalized derivatives are used instead of ordinary derivatives. These tools make it possible to establish conditions that can be used to identify optimal solutions.

A central part of the work concerns the well-known Karush–Kuhn–Tucker conditions, which provide important criteria for recognizing optimal solutions in constrained optimization. New KKT-type conditions are developed for several classes of nonsmooth optimization problems involving fuzzy information. The dissertation also shows how fuzzy optimization problems can be reformulated as multiobjective optimization problems, making it possible to use techniques from vector optimization.

In addition to the theoretical results, the dissertation considers computational methods. In particular, the Multiobjective Proximal Bundle Method is applied to the problems studied in the thesis. Computational experiments show that the method can effectively approximate solutions for the considered class of nonsmooth fuzzy optimization problems.

Overall, the dissertation provides a unified mathematical framework for studying optimization problems in which both imprecision and nonsmoothness are present. The results extend existing optimization theory and provide a foundation for further theoretical developments, numerical methods, and potential applications in areas such as engineering design, resource allocation, portfolio optimization, and planning under uncertain information.