102 KAM Mathematical Colloquium

Abstract

The moment-SOS approach (SOS=sum of squares) is a general methodology for solving optimization problems described by polynomials and compact semi-algebraic sets. In fact this methodology also applies for solving the Generalized Moment Problem (GMP) with polynomial data, of which polynomial optimization is only a very special instance (and even the simplest instance). The validity of this approach is guaranteed by powerful positivity certificates (Positivstellens"atze), breakthrough results from Real Algebraic Geometry obtained in the 1990s. We will first introduce the positivity certificates and then describe the moment-SOS approach for optimization. If time permits we will also briefly describe its application to some other applications outside optimization (as instances of the GPM with polynomial data).

O přednášejícím

Jean-Bernard Lassere studoval na univerzitach v Grenoblu a Toulouse. V soucasnosti je Directeur de Recherche CNRS na Univerzite v Toulouse (jak ustavu informatiky tak matematiky). Byl hostem prednich svetovych instituci (napr. 2 roky na Kalifornske univerzite v Berkeley, MIT, Stanford, UCLA Los Angeles, Fields institute). Je autorem vice nez 160 vedeckych praci a autorem 8 kniznich publikaci. Jeho hlavnim oborem je optimalizace, teorie pravdepodobnosti a teorie rizeni (control theory). Jedna z nejdulezitejsich hierarchii pro reseni celociselnych uloh linearniho programovani nese jeho jmeno. Je nositelem ERC grantu (projekt TAMING). Za svou cinnost ziskal nekolik oceneni spolecnosti SIAM (Lagrange prize) a spolecnosti INFORMS (Khachianova cena a  cena Johna von Neumanna, obe v roce 2015). Jeho kolokvium je venovano hlavni oblasti jeho zajmu.