Convergence analysis of a differential equation approach for solving nonlinear programming problems

We propose a system of differential equations to find a Kuhn–Tucker point of a nonlinear programming problem with both equality and inequality constraints. It is proven that the Kuhn–Tucker point of the nonlinear programming problem is an asymptotically stable equilibrium point of the proposed differential system. An iterate algorithm is constructed to find an equilibrium point of the differential system, the global convergence and local quadratic convergence rate of this algorithm are demonstrated, and illustrative examples are given.