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.
main component of my research is to develop efficient numerical methods for
solving the optimization and equilibrium models. While I am interested in
various numerical schemes, I have been focusing on
Another main component of the research is to develop theory behind the mathematical models and numerical methods. This includes various stability analysis of the problems and asymptotic analysis of statistical estimators obtained from solving approximation problems. I am excited by the underlying theoretical challenges which involve a number of areas including stochastic programming, set-valued and variational analysis, numerical optimization, statistics and nonsmooth analysis.
Written by Dr J H Renshaw,