Optimization with multivariate stochastic dominance constraints
成果类型：
Article
署名作者：
Dentcheva, Darinka; Ruszczynski, Andrzej
署名单位：
Rutgers University System; Rutgers University New Brunswick; Stevens Institute of Technology
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-007-0165-x
发表日期：
2009
页码：
111-127
关键词：
摘要：
We consider stochastic optimization problems where risk-aversion is expressed by a stochastic ordering constraint. The constraint requires that a random vector depending on our decisions stochastically dominates a given benchmark random vector. We identify a suitable multivariate stochastic order and describe its generator in terms of von Neumann-Morgenstern utility functions. We develop necessary and sufficient conditions of optimality and duality relations for optimization problems with this constraint. Assuming convexity we show that the Lagrange multipliers corresponding to dominance constraints are elements of the generator of this order, thus refining and generalizing earlier results for optimization under univariate stochastic dominance constraints. Furthermore, we obtain necessary conditions of optimality for non-convex problems under additional smoothness assumptions.