Convergence analysis of a class of nonlinear penalization methods for constrained optimization via first-order necessary optimality conditions

We propose a scheme to solve constrained optimization problems by combining a nonlinear penalty method and a descent method. A sequence of nonlinear penalty optimization problems is solved to generate a sequence of stationary points, i.e., each point satisfies a first-order necessary optimality condition of a nonlinear penalty problem. Under some conditions, we show that any limit point of the sequence satisfies the first-order necessary condition of the original constrained optimization problem.