Asymptotics of minimax stochastic programs

On a Class of Minimax Stochastic Programs

For a particular class of minimax stochastic programming models, we show that the problem can be equivalently reformulated into a standard stochastic programming problem. This permits the direct use of standard decomposition and sampling methods developed for stochastic programming. We also show that this class of minimax stochastic programs is closely related to a large family of mean-risk sto...

Uncertainties in stochastic programming models: The minimax approach

Extended abstract 50 years ago, stochastic programming was introduced to deal with uncertain values of coefficients which were observed in applications of mathematical programming. These uncertainties were modeled as random and the assumption of complete knowledge of the probability distribution of random parameters became a standard. In practice, complete knowledge of the probability distribut...

Stochastic Programming: Minimax Approach

In many applications of stochastic programming there is some uncertainty about the probability distribution P of the random parameters. The incomplete knowledge of the probability distribution can be described by assuming that P belongs to a specified class P of probability distributions. This in turn suggests to use the minimax decision rule. The first results were concerned with stochastic li...

Uncertainties in minimax stochastic programs

When using the minimax approach one tries to hedge against the worst possible distribution belonging to a specified class P . A suitable stability analysis of results with respect to the choice of this class is an important issue. It has to be tailored to the type of the minimax problem, to the considered class of probability distributions and to the anticipated input perturbations. We shall fo...

Exact Asymptotics of Minimax Bahadur Risk in Lipschitz Regression