We will address how set-valued optimization can be used to approach problems from systems biology and that way opens doorways to simplifying and systematizing many, often pragmatic frameworks in this field. We will concentrate on problems concerning the dynamic simulation of metabolic networks with potential applications ranging from personalized medicine over bio-fuel production to ecosystem biology. From the mathematical modeling viewpoint, we will underline how evolutionary principles may in this regard be interpreted as a regularization and illustrate this by some small-scale examples.
joint work with César Gutiérrez, Lidia Huerga, Christiane Tammer
In this talk, a method for scalarizing optimization problems whose final space is an ordered set is stated without assuming any additional assumption on the data of the problem. By this approach, nondominated and minimal solutions are characterized in terms of solutions of scalar optimization problems whose objective functions are the post-composition of the original objective with scalar functions satisfying suitable properties. The obtained results generalize some recent ones stated in quasi ordered sets and real topological linear spaces.
We will discuss the inverse problem of parameter identification in general saddle point problems that frequently appear in applied models. We focus on examining the role of the inf-sup condition. Assuming the saddle point problem is solvable, we study the differentiability of the set-valued parameter-to-solution map by using the first-order and the second-order contingent derivatives. We investigate the inverse problem by using the nonconvex output least-squares and the convex modified output least-squares objectives. Numerical results and applications will be presented.