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Quadratic programming (QP) is a common and important constrained optimizationproblem. Here, we derive a surprising duality between constrained optimizationwith inequality constraints -- of which QP is a special case -- and consumerresource models describing ecological dynamics. Combining this duality with arecent `cavity solution', we analyze high-dimensional, random QP where theoptimization function and constraints are drawn randomly. Our theory showsremarkable agreement with numerics and points to a deep connection betweenoptimization, dynamical systems, and ecology.

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