Variational Analysis and Optimisation Webinars, http://www.mocao.org/va-webinar/

Title: Bridges between Discrete and Continous Optimisation in Stochastic Programming

Speaker: Andrew Eberhard (RMIT University)

Abstract: For many years there has been a divide between the theoretical under pinning
of algorithmic analysis in discrete and continuous optimisation. As a case
study, stochastic optimisation provides a classic example. Here the
theoretical foundations of continuous stochastic optimisation lies in the
theory of monotone operators, operator splitting and nonsmooth analysis, none
of which appear to be applicable to discrete problems. In this talks we will
discuss the application of ideas from continuous optimisation and variational
analysis to the study of progressive hedging like methods for discrete
optimisation models. The key to the success of such approaches is the
acceptance of the existence of MIP and QMIP\ solvers that can be integrated in
to analysis as "black box solvers" that return solutions within a broader
algorithmic analysis. Here methods more familiar to continuous optimisers and
nonsmooth analysts can be used to provide proofs of convergence of both primal
and dual methods. Unlike continuous optimisation there still exists separate
primal and dual methods and analysis in the discrete context. We will discuss
this aspect and some convergent modifications that yield robust and effective
versions of these methods, long with numerical validation of their
effectiveness.

Author:	Vera Roshchina (via theBox)
Created:	02/07/2021
Updated:	02/07/2021
Theme:	Default
Copyright:	Creative Commons

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