Ann Oper Res DOI 10.1007/s10479-016-2299-9 ORIGINAL PAPER Aspects of optimization with stochastic dominance William B. Haskell 1 · J. George Shanthikumar 2 · Z. Max Shen 3 © Springer Science+Business Media New York 2016 Abstract We consider stochastic optimization problems with integral stochastic order con- straints. This problem class is characterized by an infinite number of constraints indexed by a function space of increasing concave utility functions. We are interested in effective numerical methods and a Lagrangian duality theory. First, we show how sample average approximation and linear programming can be combined to provide a computational scheme for this problem class. Then, we compute the Lagrangian dual problem to gain more insight into this problem class. Keywords Stochastic dominance · Convex optimization · Sample average approximation · Duality 1 Introduction In this paper, we emphasize the increasing concave stochastic order (≥ icv ) as a tool for risk management in stochastic optimization. ≥ icv is historically associated with risk-averse decision makers. A utility function for a risk-averse decision maker is increasing and concave, corresponding to a preference for more over less and decreasing marginal utility. ≥ icv is a comparison between two random variables defined in terms of their expected utilities over all increasing concave utility functions, and thus ≥ icv has a natural connection to risk aversion. B William B. Haskell wbhaskell@gmail.com J. George Shanthikumar jshanthi@purdue.edu Z. Max Shen shen@ieor.berkeley.edu 1 National University of Singapore, Singapore, Singapore 2 Purdue University, West Lafayette, IN, USA 3 University of California Berkeley, Berkeley, CA, USA 123