Volume 53, Number 1, January-March 2019
|Page(s)||81 - 109|
|Published online||31 January 2019|
Undecidability and hardness in mixed-integer nonlinear programming
CNRS LIX, École Polytechnique,
* Corresponding author: firstname.lastname@example.org
Accepted: 4 May 2018
We survey two aspects of mixed-integer nonlinear programming which have attracted less attention (so far) than solution methods, solvers and applications: namely, whether the class of these problems can be solved algorithmically, and, for the subclasses which can, whether they are hard to solve. We start by reviewing the problem of representing a solution, which is linked to the correct abstract computational model to consider. We then cast some traditional logic results in the light of mixed-integer nonlinear programming, and come to the conclusion that it is not a solvable class: instead, its formal sentences belong to two different theories, one of which is decidable while the other is not. Lastly, we give a tutorial on computational complexity and survey some interesting hardness results in nonconvex quadratic and nonlinear programming.
Mathematics Subject Classification: 90C11 / 90C26
Key words: Undecidability / hardness / mathematical programming
© EDP Sciences, ROADEF, SMAI 2019
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.