A constrained min-max algorithm for rival models
In the presence of rival models of the same system, a robust optimal policy can be computed that takes account of the existence of the rival models. A min-max, worst case design method is discussed. The latter is an extreme case of ordinary pooling of the models for policy optimization. In fact, it can be shown that the min-max strategy is the pooling that corresponds to the robust policy. If such a robust policy happens to have too high a political cost to be implemented, an alternative pooling can be formulated using the robust pooling as a guide. An algorithm is proposed for solving the min-max problem. This is based on the convexification of the minimization problem by means of the constraints. The algorithm essentially consists of a quadratic programming subproblem with equality and simple inequality constraints. The subproblem defines the direction of progress along which a step has to be taken. The stepsize is determined using an Armijo-type stepsize strategy that ensures sufficient progress towards the satisfaction of the first-order conditions. The latter also happens to be sufficient for optimality due to the convexification of the problem. The formulation of the problem, the robust policy formulation of the min- max approach and the convergence properties of the algorithm are discussed in another paper of the author [``A superlinearly convergent constrained min-max algorithm for rival models of the same system'', PROPE discussion paper No.96, Imperial Coll., London (1987)].
scientific article; zbMATH DE number 4055332