In this paper, we consider Newton projection method for solving the quadratic programming problem that emerges in simulation of joining process for assembly with compliant parts. This particular class of problems has specific features such as an ill-conditioned Hessian and a sparse matrix of constraints as well as a requirement for the large-scale computations. We use the projected Newton method with a quadratic rate of convergence and suggest some improvements to reduce the solving time: a method for solving the system of linear equations, so-called constraint recalculation method, and compare different approaches for step-size selection. We use the duality principle to formulate alternative forms of the minimization problem that, as a rule, can be solved faster. We describe how to solve the considered nonlinear minimization problem with the nonsmooth objective function by modifying Newton projection method and employing subgradients. In addition, we prove the convergence of the suggested algorithm. Finally, we compare Newton projection method with the other quadratic programming techniques on a number of assembly simulation problems.

在本文中，我们考虑牛顿投影法来解决二次规划问题，该二次规划问题出现在与柔性零件装配的连接过程模拟中。这类特定问题具有特定特征，例如病态 Hessian 矩阵和稀疏约束矩阵，以及对大规模计算的要求。我们使用具有二次收敛速度的投影牛顿法，并提出一些改进以减少求解时间：求解线性方程组的方法，即所谓的约束重新计算方法，并比较不同的步长选择方法。我们使用对偶原理来制定最小化问题的替代形式，通常可以更快地解决这些问题。我们描述了如何通过修改牛顿投影方法和使用次梯度来解决所考虑的非线性最小化问题与非光滑目标函数。此外，我们证明了建议算法的收敛性。最后，我们将牛顿投影法与其他二次规划技术在一些装配仿真问题上进行了比较。