The Generalized Moment problem is an infinite-dimensional LP which takes one line to state in compact form, and whose list of potential important applications is almost endless. However, in full generality the GMP is not solvable. On the other hand, if its data consist of polynomials (or more generally semi-algebraic functions) and semi-algebraic sets then one is able to define a systematic numerical scheme, the Moment-SOS hierarchy, to approximate its optimal value as closely as desired. (One has to solve a sequence of semidefinite-relaxations of increasing size.) It was initially designed for solving global optimization problem and in this context finite convergence of the hierarchy is « generic » and global minimizers can be extracted.
I will describe the Moment-SOS approach and shows how it can be applied to help solve several problems outside optimization, e.g. in computational geometry, probability & statistics, control & optimal control, as well as analysis of certain non-linear PDEs.
JB Lasserre graduated from "Ecole Nationale Superieure d'Informatique et Mathematiques Appliquees"
(ENSIMAG) in Grenoble (France), and got his PhD (1978) and "Doctorat d'Etat" (1984) degrees
both from Paul Sabatier University in Toulouse (France). He has been at LAAS-CNRS in Toulouse
since1980, wherehe is currently Directeur de Recherche. he is also a member of IMT,
the Institute of Mathematics of Toulouse. He was a one year visitor (1978-79 and 1985-86) at the
Electrical Engineering Dept. of the University of California at Berkeley with a fellowship from
INRIA and NSF. He has done several one-month visits to Stanford University, MIT,
He wrote about 180 papers and authored or co-authored eight books.