2011 Winter School: Wrap Up

The 2011 Winter School on Global Optimisation: theory and application was hosted by the University of Queensland. This year, two advanced courses were offered aimed at postgraduate students and researchers in mathematics and related disciplines and were presented by distinguished researchers.

In addition to these courses, participants had the opportunity to present their own research during the program. Each participant presented a seminar of 20 minutes on a topic related to their research.

COURSES

MOMENTS, POSITIVE POLYNOMIALS AND THEIR APPLICATIONS 

Dr Jean Lasserre

This course introduced a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriate cones, standard duality in convex optimisation nicely expresses the duality between moments and positive polynomials.  On the application side, a particular emphasis is put on (global) polynomial optimisation but if time permits, other important applications (in e.g. probability, optimal control, mathematical finance, multivariate integration, etc.) will be also described in some details.

COMPETITIVE MARKOV DECISION PROCESS

Professor Jezry Filar

This course was devoted to a unified treatment of both Markov Decision Process and Stochastic Games. It examined these processes from the standpoints of modelling and of optimisation, providing newcomers to the field with an accessible account of algorithms, theory and application.