This paper discusses a class of two-block nonconvex smooth optimization problems with nonlinear constraints. Based on a quadratically constrained quadratic programming (QCQP) approximation, an augmented Lagrangian function (ALF), and a Lagrangian splitting technique into small-scale subproblems, we propose a novel sequential quadratic programming (SQP) algorithm. First, inspired by the augmented Lagrangian method (ALM), we penalize the quadratic equality constraints associated with the QCQP approximation subproblem in its objective by means of the ALF, and then split the resulting subproblem into two small-scale ones, but both of them are not quadratic programming (QP) due to the square of the quadratic equality constraints in the objective. Second, by ignoring the three-order infinitesimal arising from the squared term, the two small-scale subproblems are reduced to two standard QP subproblems, which can yield an improved search direction. Third, taking the ALF of the discussed problem as a merit function, the next iterate point is generated by the Armijo line search. As a result, a new SQP method, called QCQP-based splitting SQP method, is proposed. Under suitable conditions, the global convergence, strong convergence, iteration complexity and convergence rate of the proposed method are analyzed and obtained. Finally, preliminary numerical experiments and applications were carried out, and these show that the proposed method is promising.

本文讨论了一类具有非线性约束的两块非凸光滑优化问题。基于二次约束二次规划（QCQP）逼近，增强拉格朗日函数（ALF）和拉格朗日拆分技术将其分解为小规模子问题，我们提出了一种新颖的顺序二次规划（SQP）算法。首先，受增强拉格朗日方法（ALM）的启发，我们通过ALF对与QCQP逼近子问题相关联的二次等式约束进行了惩罚，然后将所得子问题分为两个小规模问题，但它们都由于目标中二次等式约束的平方，所以它们不是二次规划（QP）。其次，通过忽略平方项引起的三阶无穷小，这两个小规模子问题被简化为两个标准QP子问题，可以改善搜索方向。第三，将讨论的问题的ALF作为优值函数，由Armijo线搜索生成下一个迭代点。结果，提出了一种新的SQP方法，称为基于QCQP的拆分SQP方法。在适当的条件下，分析并获得了该方法的全局收敛性，强收敛性，迭代复杂度和收敛速度。最后，进行了初步的数值实验和应用，表明所提出的方法是有希望的。结果，提出了一种新的SQP方法，称为基于QCQP的拆分SQP方法。在适当的条件下，分析并获得了该方法的全局收敛性，强收敛性，迭代复杂度和收敛速度。最后，进行了初步的数值实验和应用，表明所提出的方法是有希望的。结果，提出了一种新的SQP方法，称为基于QCQP的拆分SQP方法。在适当的条件下，分析并获得了该方法的全局收敛性，强收敛性，迭代复杂度和收敛速度。最后，进行了初步的数值实验和应用，表明所提出的方法是有希望的。