Mehta Pankaj, Cui Wenping, Wang Ching-Hao, Marsland Robert
Physics Department, Boston University, Boston, Massachusetts 02215, USA.
Physics Department, Boston College, Chestnut Hill, Massachusetts 02467, USA.
Phys Rev E. 2019 May;99(5-1):052111. doi: 10.1103/PhysRevE.99.052111.
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.
二次规划（QP）是一个常见且重要的约束优化问题。在此，我们推导出了具有不等式约束的约束优化（QP是其特殊情况）与描述生态动力学的消费者资源模型之间令人惊讶的对偶性。将这种对偶性与最近的“腔解”相结合，我们分析了高维随机QP，其中优化函数和约束是随机抽取的。我们的理论与数值结果显示出显著的一致性，并指出了优化、动力系统和生态学之间的深刻联系。
