Constrained Primal-Dual Dynamics for QCQP with Applications to Economic Dispatch

We develop concise primal-dual dynamics for a class of Quadratically Constrained Quadratic Programming problems in power system optimization. Using a constrained La-grangian reformulation of the problem and the classical stability result of Lyapunov, we establish the asymptotic convergence of the primal-dual dynamics. We demonstrate the efficiency of the proposed method on an economic power dispatch problem with transmission losses and we suggest a neural network architecture for real-time optimization.