Lagrange principle in quadratic optimal control problems with infinite horizon

We consider a quadratic optimal control problem on an infinite time interval with integral quadratic equality and inequality constraints. For this (generally, nonconvex) problem, we justify the Lagrange constraint removal principle and the duality relation. The obtained result is based on the general theory of extremal problems, namely, on necessary second-order extremum conditions. © Pleiades Publishing, Ltd., 2009.