As for nonlinear programming problem with equality constraints, a general method of solution is to gradually increase penalty factor of Lagrange function and to renew Lagrange multipliers in the iteration of each cycle. If penalty factor is sufficiently large or is close to local optimal solution, the second-order sufficient conditions are satisfied.This paper use the corresponding method for inequality-constrained problems. Global convergence to an optimal solution is established in the convex case for an arbitrary penalty factor and without the requirement of an exact minimum in the iteration of each cycle.Furthermore, the Lagrange multipliers are proved to converge.