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

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.

SUBMITTER: Mehta P 

PROVIDER: S-EPMC6717431 | biostudies-literature | 2019 May

REPOSITORIES: biostudies-literature