.. _BIGM_TPWRS:

Solving Linear Bilevel Problems Using Big-Ms: Not All That Glitters Is Gold
=================================================================================
.. sectionauthor:: Salvador Pineda <spinedamorente@gmail.com>

This is a summary of the work that can be found in `[1]`_. Open Access pdf is available at `[2]`_.

Abstract
--------

The most common procedure to solve a linear bilevel problem in the PES community is, by far, to transform it into an equivalent  single-level problem by replacing the lower level with its KKT optimality conditions. Then, the complementarity conditions are reformulated using additional binary variables and large enough constants (big-Ms) to cast the single-level problemas a mixed-integer linear program that can be solved using optimization  software. In most cases, such large constants are tuned by  trial and error. We show, through a counterexample, that this  widely used trial-and-error approach may lead to highly suboptimal solutions. Then, further research is required to properly select big-M values to solve linear bilevel problems.


Citation
--------

If you would like to cite this work, please use the following citation: 

	S. Pineda and J. M. Morales, `Solving Linear Bilevel Problems Using Big-Ms: Not All That Glitters Is Gold`, `IEEE Transactions on Power Systems`, vol. 34, no. 3, pp. 2469--2471, May 2019.

You can use this bibtex entry: 

.. code-block:: latex

   @article{pineda2019solving,
     title={Solving linear bilevel problems using big-Ms: not all that glitters is gold},
     author={Pineda, Salvador and Morales, Juan Miguel},
     journal={IEEE Transactions on Power Systems},
     volume={34},
     number={3},
     pages={2469--2471},
     year={2019},
     publisher={IEEE}
   }

.. _[1]: https://ieeexplore.ieee.org/document/8610245
.. _[2]: https://drive.google.com/uc?export=download&id=1lWkW-ukmI8WYhCPQ9a9qhP2Nbsyqtpy_