Presentation
My name is Hubert Villuendas and I am a PhD student in applied mathematics at the Jean Kuntzmann Laboratory and the Grenoble Computer Science Laboratory, under the supervision of Jérôme Malick and Mathieu Besançon.
My thesis focuses on methods and applications of mixed-integer conic optimisation. More specifically, mixed-integer conic optimisation is a class of optimisation problems where decision variables take integer values and constraints can be expressed as belonging to a convex cone \(\mathcal{K}\subseteq\mathbb{R}^m\) :
\[\left[\begin{array}{rll} \text{minimize} & c^\top x &\\ \text{subject to} & Ax-b\in \mathcal{K} &\\ & x_i\in\mathbb{Z}^p\times\mathbb{R}^{n-p} & \forall i\in [\![n]\!] \end{array}\right.\]where \(A\in\mathbb{R}^{n\times m}\) and \(b\in\mathbb{R}^m\).
Conic optimisation generalises linear optimisation by introducing structured non-linearities that capture a large number of essential problems in operational research, combinatorial optimisation, and data science.