Robust optimization is a framework for modeling optimization problemsinvolving data uncertainty and during the last decades has been an area ofactive research. If we focus on linear programming (LP) problems with i)uncertain data, ii) binary decisions and iii) hard constraints within anellipsoidal uncertainty set, this paper provides a different interpretation oftheir robust counterpart (RC) inspired from decomposition techniques. This newinterpretation allows the proposal of an ad-hoc decomposition technique tosolve the RC problem with the following advantages: i) it improvestractability, specially for large-scale problems, and ii) it provides the exactprobability of constraint violation in case the probability distribution ofuncertain parameters are completely defined by using first and second-orderprobability moments. An attractive aspect of our method is that it decomposesthe second-order cone programming problem, associated with the robustcounterpart, into a linear master problem and different quadraticallyconstrained problems (QCP) of considerable lower size. The optimal solution isachieved through the solution of these master and subproblems within aniterative scheme based on cutting plane approximations of the second-order coneconstraints. In addition, proof of convergence of the iterative method isgiven.
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