[Dottorcomp] Seminari di Matematica Applicata. Giovedì 9 giugno. Pietro Belotti.

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Giovedì 9 giugno 2022, alle ore 15.00 precise, presso l'aula Beltrami del
Dipartimento di Matematica,

Pietro Belotti (Politecnico di Milano)terrà un seminario dal titolo:

Convex hull of a monomial on a two-variable conic domain

Il seminario verrà anche trasmesso in diretta su zoom al link:

https://us02web.zoom.us/j/83344185446?pwd=RHRGai91RkZQTjg0eEVRMWQ5WXFjZz09

Abstract.
We consider a monomial function with real exponents, which is of interest
in optimization. Specifically, global optimization solvers need tight
convex relaxations of sets defined by nonconvex functions to find a valid
lower bound. The convex hull of the monomial in two variables on a bounding
box is known for some special cases, but unknown in general. We discuss the
convex hull of a generic monomial in two variables that, rather than being
restricted to a bounding box, is restricted to a two-variable cone with the
origin as its vertex. We then look at how to compute the volume of such
convex hull, which is also of interest in global optimization: in fact
branching operations of branch-and-bound solvers have a great impact in
solver efficiency, in particular some branching techniques that aim at
minimizing the total resulting volume of the two new subproblems.
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Pagina web dei Seminari di Matematica Applicata
https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/
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