Linear programming approach to nonlinear deterministic and stochastic control problems: perturbations methods and numerical analysis
(V Gaitsgory, V Ejov, J Filar, P Howlett with C. Pearce, J.-P. Aubin, K. Avrachenkov, V. Borkar, F. Colonius, P. Dupuis, H. Frankowska, H Kushner and M. Quincampoix)
We propose to study a range of important nonlinear dynamical control problems (NDCP) by embedding them in optimisation problems over sets of occupational measures and equivalently reformulating them as certain infinite-dimensional linear programming (IDLP) problems. We will use the IDLP formulations for characterization of optimality, viability and controllability of NDCP solutions and will develop perturbation methods based on analogous methods for the induced IDLP problems. We will numerically analyse NDCP by approximating their IDLP counterparts with readily solvable finite-dimensional LP problems. In the process, perturbation methods will be developed for certain operators and for some classical combinatorial optimization problems.
Funding
ARC Linkage International Grant (2008-2010), “Linear programming approach
to nonlinear deterministic and stochastic control problems: perturbations
methods and numerical analysis”, Leading CI: Vladimir Gaitsgory
Collaborators: Australian Investigators: A/ Prof V. Ejov (CI), Prof J.
Filar (CI), Prof P. Howlett (CI) and Prof C. Pearce (CI) Overseas
Investigators: Prof J.-P. Aubin, LASTRE, Paris, France; Dr K. Avrachenkov,
Sophia Antipolis, France; Prof V. Borkar, Tata Inst. of Fundamental
Research, Mumbai, India; Prof F. Colonius, University of Augsburg, Augsburg,
Germany; Prof P. Dupuis, Brown University, Providence, USA; Prof H.
Frankowska , Ecole Polytechnique, Paris, France; Prof H. Kushner, Brown
University, Providence, USA; Prof M. Quincampoix, Universite de Bretagne
Occidentale, France