Semi-infinite probabilistic optimization: first-order stochastic dominance constrain

Abstract

We consider stochastic optimization problems involving a continuum of probabilistic constraints. They are equivalent to stochastic dominance constraints of first order, frequently called stochastic ordering constraints. We develop necessary and sufficient conditions of optimality for these models. We show that the Lagrange multipliers corresponding to dominance constraints can be identified with piecewise constant nondecreasing utility functions. We also show that the convexification of stochastic ordering relation is equivalent to second-order stochastic dominance under rather weak assumptions.

Keywords:

• Stochastic programming
• Stochastic ordering
• Semi-infinite optimization
• Chance constraints
• Duality
• Risk
• Convexification
• Generalized concavity
• Mathematics Subject Classifications 2000: 90C15
• 90C34
• 60E15

Acknowledgement

The research is supported by the NSF awards DMS-0303545, DMS-0303728, DMI-0354500 and DMI-0354678.

Notes

E-mail: [email protected]

Additional information

Notes on contributors

Andrzej Ruszczyński

E-mail: [email protected]