Abstract
A vector optimization problem is studied, whose objective function is a vector of distribution functions depending on a vector of decision variables. Properties of the model are investigated and a scalar representation in terms of the joint distribution function is proposed. Furthermore, assuming to have only empirical estimates of the true distribution functions, we get a sequence of approximate problems and convergence results of the level sets and optimal solution set are proved.
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Redaelli, G. (2001). Vector Stochastic Optimization Problems. In: Hadjisavvas, N., Martínez-Legaz, J.E., Penot, JP. (eds) Generalized Convexity and Generalized Monotonicity. Lecture Notes in Economics and Mathematical Systems, vol 502. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56645-5_26
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DOI: https://doi.org/10.1007/978-3-642-56645-5_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41806-1
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