<p>The sequential quadratic programming (SQP) method has shown remarkable performance for addressing nonlinear optimization problems. However, it typically requires the quadratic programming (QP) subproblems to be feasible. To overcome this limitation, various approaches introducing penalizations or perturbations to the QP subproblems have been developed. In this study, we propose a novel natural SQP algorithm that iterates through a stationary point of the classical QP subproblem, specifically the minimizer closest to the feasible region. This approach ensures global convergence under standard assumptions by identifying a solution with the least constraint violation. The resulting solution minimizes the objective function within the set of minimizers for constraint violation. Furthermore, the proposed method exhibits a quadratic convergence rate. When the original problem is feasible, our assumptions and conclusions align with those of the classical SQP method. Numerical experiments validate the effectiveness and demonstrate the superior performance of the proposed algorithm.</p>