ï»¿A Multilevel Search Algorithm for the Maximization of Submodular Functions
AbstractWe consider the objective function of a simple recourse problem with fixed technology matrix and integer second-stage variables. Separability due to the simple recourse structure allows to study a one-dimensional version instead. Based on an explicit formula for the objective function, we derive a complete description of the class of probability density functions such that the objective function is convex. This result is also stated in terms of random variables. Next, we present a class of convex approximations of the objective function, which are obtained by perturbing the distributions of the right-hand side parameters. We derive a uniform bound on the absolute error of the approximation. Finally, we give a representation of convex simple integer recourse problems as continuous simple recourse problems, so that they can be solved by existing special purpose algorithms
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Bibliographic InfoPaper provided by University of Groningen, Research Institute SOM (Systems, Organisations and Management) in its series Research Report with number 04A20.
Date of creation: 2004
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