Undecidability and hardness in mixed-integer nonlinear programming - Archive ouverte HAL
Article Dans Une Revue RAIRO - Operations Research Année : 2019

Undecidability and hardness in mixed-integer nonlinear programming

Résumé

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.
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Dates et versions

hal-02104836 , version 1 (19-04-2019)

Identifiants

Citer

Leo Liberti. Undecidability and hardness in mixed-integer nonlinear programming. RAIRO - Operations Research, 2019, 53 (1), pp.81-109. ⟨10.1051/ro/2018036⟩. ⟨hal-02104836⟩
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