A Discrete Min-Max Algorithm: Risk Management with Rival Scenarios

Berç Rustem
Imperial College, London
br@doc.ic.ac.uk

Abstract

In the presence of rival scenarios, such as forecasts, or rival decision models purporting to represent the same system, the optimal decision needs to take account of all possible representations. The discrete min-max problem arises when statistical or economic analysis cannot rule out all but one of the rival possibilities. We then have to consider the optimal strategy corresponding to the worst-case scenario.

In this paper, we discuss an approach using an augmented Lagrangian formulation to directly solve the min-max problem with equality and inequality constraints. The algorithm involves a sequential quadratic programming subproblem, an adaptive penalty parameter selection rule, a stepsize strategy, convergent to unit steps, that ensures progress towards optimality and feasibility of the constraints.