An inexact first-order method for constrained nonlinear optimization

The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the computational cost needed for each iteration. A penalty parameter updating strategy during the process of solving the subproblem enables the algorithm to automatically detect infeasibility. Global convergence for both feasible and infeasible cases is proved. Complexity analysis for the KKT residual is also derived under mild assumptions. Numerical experiments exhibit the ability of the proposed algorithm to rapidly find inexact optimal solution through cheap computational cost.