VA & Opt Webinar: Andrew Eberhard

Title: Bridges between Discrete and Continous Optimisation in Stochastic Programming

Speaker: Andrew Eberhard (RMIT University)

Date and Time: June 30th, 2021, 17:00 AEST (Register here for remote connection via Zoom)

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.