††††††††††† Professor of Operational Research
School of Mathematical Sciences
University of Southampton
Southampton SO17 1BJ
+44 (0)23 8059 3657
+44 (0)23 8059 5147
Mathematics Building, Room 10013
Internal Phone Extension
My recent interest is in optimal decision making problems that involve uncertain data. This includes developing and/or investigating new mathematical models which capture the uncertainty and other features such as competition, equilibrium and hierarchical relationships between decision makers.† Typical examples are stochastic principal agent models (Stackelberg leader follower models), stochastic Nash equilibrium models, stochastic bilevel programming models, stochastic mathematical programs with equilibrium constraints (SMPEC) models and stochastic equilibrium programs with equilibrium constraints (SEPEC) models. The new stochastic optimization and equilibrium models have many applications in the study of optimal strategy and competition in energy industry, stability of power system/networks, equilibrium of transportation networks, capacity expansion/investment, optimal policy setting, engineering design etc. I am also interested in risk management models such as condition value at risk models and dominance constrained stochastic program models.
An important component of the research is to identify uncertainties and quantify them. This is not an easy task for many so-call data-driven problems where the size of uncertain data could be small or very large (in which case we will have to be selective). A popular approach to handle this is distributionally robust optimization (DRO) which uses partial information to construct a set of distributions based on empirical data, computer simulation and subjective judgement and base optimal decision on the worst probability distribution to mitigate the risk amid incomplete information of uncertainty. Over the past few years, I have been working on this exciting research area with particular focus on quantitative stability analysis which quantifies the difference between the true unknown probability distribution and approximation based on distributionally robust approach and its impact on the optimal decision making.†† I refer interested reader to the website of workshop at Banff https://www.birs.ca/events/2018/5-day-workshops/18w5102 for an overview of the recent development of DRO.
More recently, I am looking into so-called preference robust optimization where the underlying uncertainty arises from decision makerís utility preferences or risk attitudes. This is a new stream of research which focuses on endogenous rather than exogenous uncertainty as in distributionally robust optimization. It is built on Von NeumannĖMorgenstern expected utility theory which underpins modern economics and stochastic dominance. One of the main challenges is how to elicit decision makerís preference either because there is limited information or the prospect space is too large. There are also many other challenges such as developing appropriate robust models and tractable numerical schemes.
Written by Dr J H Renshaw,