Solving Optimization Problems with Diseconomies of Scale via Decoupling

@article{Makarychev2014SolvingOP,
title={Solving Optimization Problems with Diseconomies of Scale via Decoupling},
author={Konstantin Makarychev and Maxim Sviridenko},
journal={2014 IEEE 55th Annual Symposium on Foundations of Computer Science},
year={2014},
pages={571-580}
}

We present a new framework for solving optimization problems with a diseconomy of scale. In such problems, our goal is to minimize the cost of resources used to perform a certain task. The cost of resources grows superlinearly, as x<sup>q</sup>, q ≥ 1, with the amount x of resources used. We define a novel linear programming relaxation for such problems, and then show that the integrality gap of the relaxation is A<sub>q</sub>, where A<sub>q</sub> is the q-th moment of the Poisson random… CONTINUE READING