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arXiv · 1701.01419

On Convex Programming Relaxations for the Permanent

Damian Straszak·Nisheeth K. Vishnoi
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Abstract

In recent years, several convex programming relaxations have been proposed to estimate the permanent of a non-negative matrix, notably in the works of Gurvits and Samorodnitsky. However, the origins of these relaxations and their relationships to each other have remained somewhat mysterious. We present a conceptual framework, implicit in the belief propagation literature, to systematically arrive at these convex programming relaxations for estimating the permanent -- as approximations to an exponential-sized max-entropy convex program for computing the permanent. Further, using standard convex programming techniques such as duality, we establish equivalence of these aforementioned relaxations to those based on capacity-like quantities studied by Gurvits and Anari et al.

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Damian Straszak, Nisheeth K. Vishnoi. 2017-01-05. On Convex Programming Relaxations for the Permanent. https://arxiv.org/abs/1701.01419

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