A cutting-surface method for uncertain linear programs with polyhedral stochastic dominance constraints

Tito Homem-De-mello, Sanjay Mehrotra

Producción científica: Contribución a una revistaArtículorevisión exhaustiva

46 Citas (Scopus)

Resumen

In this paper we study linear optimization problems with a newly introduced concept of multidimensional polyhedral linear second-order stochastic dominance constraints. By using the polyhedral properties of this dominance condition, we present a cutting-surface algorithm and show its finite convergence. The cut generation problem is a difference of convex functions (DC) optimization problem. We exploit the polyhedral structure of this problem to present a novel branch-and-cut algorithm that incorporates concepts from concave minimization and binary integer programming. A linear programming problem is formulated for generating concavity cuts in our case, where the polyhedra are unbounded. We also present duality results for this problem relating the dual multipliers to utility functions, without the need to impose constraint qualifications, which again is possible because of the polyhedral nature of the problem. Numerical examples are presented showing the nature of solutions of our model.

Idioma originalInglés
Páginas (desde-hasta)1250-1273
Número de páginas24
PublicaciónSIAM Journal on Optimization
Volumen20
N.º3
DOI
EstadoPublicada - 2009
Publicado de forma externa

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