Geodesic
Computation of exponential integrals
Zapiski Nauchnykh Seminarov POMI, Computational complexity theory. Part 5, Tome 192 (1991), pp. 149-162

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Let $P\subset\mathbb{R}^d$ be a convex full-dimensional polytope and $f:\mathbb{R}^d\mapsto\mathbb{R}$ be a linear function. The computational complexity of the integral $\int_P\exp\{f(x)\}d\,x$ is studied. It is shown that these integrals are subjected to certain non-trivial algebraic relations that makes it possible to design polynomial-time algorithms for some polytopes. Applications of exponential integrals to computation of volume and to non-linear programming are given. 
@article{ZNSL_1991_192_a6,
     author = {A. I. Barvinok},
     title = {Computation of exponential integrals},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {149--162},
     publisher = {mathdoc},
     volume = {192},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1991_192_a6/}
}
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A. I. Barvinok. Computation of exponential integrals. Zapiski Nauchnykh Seminarov POMI, Computational complexity theory. Part 5, Tome 192 (1991), pp. 149-162. http://geodesic.mathdoc.fr/item/ZNSL_1991_192_a6/