Constrained optimization as ecological dynamics with applications to random quadratic programming in high dimensions
arXiv:1809.04221 · doi:10.1103/PhysRevE.99.052111
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.
12 pages, 3 figures with appendix
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