We propose an inexact nonmonotone successive quadratic programming (SQP) algorithm for solving nonlinear programming problems with equality constraints and bounded variables. Regarding the value of the current feasibility violation and the minimum value of its linear approximation over a trust region, several scenarios are envisaged. In one scenario, a possible infeasible stationary point is detected. In other scenarios, the search direction is computed using an inexact (truncated) solution of a feasible strictly convex quadratic program (QP). The search direction is shown to be a descent direction for the objective function or the feasibility violation in the feasible or infeasible iterations, respectively. A new penalty parameter updating formula is proposed to turn the search direction into a descent direction for an ${\ell }_1$-penalty function. In certain iterations, an accelerator direction is developed to obtain a superlinear local convergence rate of the algorithm. Using a nonmonotone filter strategy, the global convergence of the algorithm and a superlinear local rate of convergence are guaranteed. The main advantage of the algorithm is that the global convergence of the algorithm is established using inexact solutions of the QPs. Furthermore, the use of inexact solutions instead of exact solutions of the subproblems enhances the robustness and efficiency of the algorithm. The algorithm is implemented using MATLAB and the program is tested on a wide range of test problems from the CUTEst library. Comparison of the obtained numerical results with those obtained by testing some similar SQP algorithms affirms the efficiency and robustness of the proposed algorithm.

我们提出了一种不精确的非单调连续二次规划（SQP）算法，用于解决具有相等约束和有界变量的非线性规划问题。关于当前可行性违反的价值及其在信任区域上线性近似的最小值，设想了几种方案。在一种情况下，检测到可能的不可行固定点。在其他情况下，使用可行的严格凸二次规划（QP）的不精确（截断）解来计算搜索方向。搜索方向分别显示为目标函数或可行或不可行迭代中违反可行性的下降方向。提出了一种新的惩罚参数更新公式，可以将搜索方向转换为下降方向。${\ell }_{\mathrm{1个}}$-惩罚功能。在某些迭代中，开发加速器方向以获得算法的超线性局部收敛率。使用非单调滤波器策略，可以保证算法的全局收敛性和超线性局部收敛率。该算法的主要优点是使用QP的不精确解建立了算法的全局收敛性。此外，使用不精确的解决方案代替子问题的精确解决方案可以提高算法的鲁棒性和效率。该算法是使用MATLAB实施的，并且该程序已在CUTEst库中针对各种测试问题进行了测试。将获得的数值结果与通过测试一些类似的SQP算法获得的数值结果进行比较，证实了所提算法的效率和鲁棒性。