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Multi-objective risk-averse two-stage stochastic programming problems

Cagin Ararat(cararat***at***bilkent.edu.tr)
Ozlem Cavus(ozlem.cavus***at***bilkent.edu.tr)
Ali Irfan Mahmutogullari(a.mahmutogullari***at***bilkent.edu.tr)

Abstract: We consider a multi-objective risk-averse two-stage stochastic programming problem with a multivariate convex risk measure. We suggest a convex vector optimization formulation with set-valued constraints and propose an extended version of Benson's algorithm to solve this problem. Using Lagrangian duality, we develop scenario-wise decomposition methods to solve the two scalarization problems appearing in Benson's algorithm. Then, we propose a procedure to recover the primal solutions of these scalarization problems from the solutions of their Lagrangian dual problems. Finally, we test our algorithms on a multi-asset portfolio optimization problem under transaction costs.

Keywords: multivariate risk measure, multi-objective risk-averse two-stage stochastic programming, risk-averse scalarization problems, convex Benson algorithm, nonsmooth optimization, bundle method, scenario-wise decomposition

Category 1: Stochastic Programming

Citation:

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Entry Submitted: 11/15/2017
Entry Accepted: 11/24/2017
Entry Last Modified: 11/15/2017

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