Constrained optimization as ecological dynamics with applications to random quadratic programming in high dimensions

Pankaj Mehta; Wenping Cui; Ching-Hao Wang; Robert Marsland III

doi:10.1103/physreve.99.052111

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arXiv · 1809.04221

Constrained optimization as ecological dynamics with applications to random quadratic programming in high dimensions

Pankaj Mehta·Wenping Cui·Ching-Hao Wang·Robert Marsland III

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Abstract

Quadratic programming (QP) is a common and important constrained optimization problem. Here, we derive a surprising duality between constrained optimization with inequality constraints -- of which QP is a special case -- and consumer resource models describing ecological dynamics. Combining this duality with a recent `cavity solution', we analyze high-dimensional, random QP where the optimization function and constraints are drawn randomly. Our theory shows remarkable agreement with numerics and points to a deep connection between optimization, dynamical systems, and ecology.

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cond-mat.stat-mech cond-mat.dis-nn math.OC q-bio.PE

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Pankaj Mehta, Wenping Cui, Ching-Hao Wang, Robert Marsland III. 2018-09-12. Constrained optimization as ecological dynamics with applications to random quadratic programming in high dimensions. https://doi.org/10.1103/physreve.99.052111

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