Optimization Online


Moment-SOS hierarchy and exit time of stochastic processes

Didier Henrion(henrion***at***laas.fr)
Mauricio Junca(mauricio.junca***at***gmail.com)
Mauricio Velasco(mauvelasco***at***gmail.com)

Abstract: The moment sum of squares (moment-SOS) hierarchy produces sequences of upper and lower bounds on functionals of the exit time solution of a polynomial stochastic differential equation with polynomial constraints, at the price of solving semidefinite optimization problems of increasing size. In this note we use standard results from elliptic partial differential equation analysis to prove convergence of the bounds produced by the hierarchy. We also use elementary convex analysis to describe a super- and sub-solution interpretation dual to a linear formulation on occupation measures. The practical relevance of the hierarchy is illustrated with numerical examples.


Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )


Download: [PDF]

Entry Submitted: 01/14/2021
Entry Accepted: 02/01/2021
Entry Last Modified: 01/14/2021

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society