## The complexity of approximating a nonlinear program (1992)

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Venue: | IBM Research Report RC 17831 |

Citations: | 57 - 3 self |

### BibTeX

@INPROCEEDINGS{Bellare92thecomplexity,

author = {Mihir Bellare and Phillip Rogaway},

title = {The complexity of approximating a nonlinear program},

booktitle = {IBM Research Report RC 17831},

year = {1992}

}

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### Abstract

We consider the problem of finding the maximum of a multivariate polynomial inside a convex polytope. We show that there is no polynomial time approximation algorithm for this problem, even one with a very poor guarantee, unless P = NP. We show that even when the polynomial is quadratic (i.e. quadratic programming) there is no polynomial time approximation unless NP is contained in quasi-polynomial time. Our results rely on recent advances in the theory of interactive proof systems. They exemplify an interesting interplay of discrete and continuous mathematics—using a combinatorial argument to get a hardness result for a continuous optimization problem.