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.

本文的主要重点是设计一种不精确的一阶算法来解决受约束的非线性优化问题。通过控制子问题解决方案的不精确性，我们可以显着降低每次迭代所需的计算成本。求解子问题过程中的惩罚参数更新策略使算法能够自动检测不可行性。证明了可行和不可行情况的全局收敛。KKT 残差的复杂性分析也是在温和假设下得出的。数值实验证明了所提出的算法能够通过廉价的计算成本快速找到不精确的最优解。