Immanuel Bomze

Who is Immanuel Bomze?

Immanuel Bomze is an Austrian mathematician. In his Ph.D. thesis, he completely classified all possible flows of the generalized Lotka–Volterra dynamics on the plane, employing equivalence of this dynamics to the 3-type replicator equation.

In “Non-cooperative two-person games in biology: a classification” and his book jointly authored with B. M. Pötscher, he popularized the field of evolutionary game theory which at that time received most attention within Theoretical Biology, among researchers in Economics and Social Sciences.

Around the turn of the millennium, he coined, together with his co-authors, the now widely used terms "Standard Quadratic Optimization" and "Copositive Optimization" or "Copositive Programming". While the further deals with the simplest problem class in non-linear optimization with an NP-hard complexity, copositive optimization allows a conic reformulation of these hard problems as a linear optimization problem over a closed convex cone of symmetric matrices, a so-called conic optimization problem. In this type of problems, the full extent of complexity is put into the cone constraint, while structural constraints and also the objective function are linear and therefore easy to handle.