A special class of quadratic programming (QP) problems is considered in this paper. This class emerges in simulation of assembly of large-scale compliant parts, which involves the formulation and solution of contact problems. The considered QP problems can have up to 20,000 unknowns, the Hessian matrix is fully populated and ill-conditioned, while the matrix of constraints is sparse. Variation analysis and optimization of assembly process usually require massive computations of QP problems with slightly different input data. The following optimization methods are adapted to account for the particular features of the assembly problem: an interior point method, an active-set method, a Newton projection method, and a pivotal algorithm for the linear complementarity problems. Equivalent formulations of the QP problem are proposed with the intent of them being more amenable to the considered methods. The methods are tested and results are compared for a number of aircraft assembly simulation problems.

本文考虑一类特殊的二次规划（QP）问题。该课程出现在大型兼容零件的装配模拟中，涉及接触问题的制定和解决。所考虑的QP问题最多可包含20,000个未知数，Hessian矩阵已完全填充且条件不佳，而约束矩阵则很少。变异分析和装配过程的优化通常需要对输入数据稍有不同的QP问题进行大量计算。下列优化方法适用于解决装配问题的特殊特征：内点法，有效集法，牛顿投影法和线性互补问题的关键算法。提出了QP问题的等效公式，其意图是更适合所考虑的方法。对这些方法进行了测试，并比较了许多飞机装配仿真问题的结果。