A superlinearly convergent constrained min-max algorithm for rival models of the same system
In the presence of rival models of the same economic system, an optimal policy can be computed that takes account of the existence of all the models. A min-max, worst-case design, problem is formulated and subsequently restated as an alternative min-max problem. A numerical example of this approach is discussed by \textit{R. G. Becker}, \textit{B. Dwolatzky}, \textit{E. Karakitsos} and the author [Econ. J. 96, 425-448 (1986)]. The latter is an extreme case of an ordinary pooling of the models for policy optimization. In fact, it is shown that the min-max strategy is the pooling that corresponds to the robust policy. If such 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. This 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 for the convexification of the problem. The global convergence of the algorithm is established. The conditions are derived under which the stepsize converges to unity and the algorithm achieves a Q-superlinear convergence rate.
scientific article; zbMATH DE number 4097089
scientific article