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A projection algorithm for positive definite linear complementarity problems with applications

机译：正定线性互补问题的投影算法及其应用

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摘要

A projection algorithm for positive definite linear complementarity problems is introduced. The algorithm incorporates the basic idea of gradient projection algorithms. A new descent direction, which will be referred to as the vector of centers, is used instead of the negative of the objective function gradient. This descent direction is kept fixed throughout the iterations, thus reducing the computational effort of computing a search direction by O(n~2) per step. The algorithm exploits the ellipsoid algorithm to find an advanced starting point on the boundary of the feasible region. Accordingly, the algorithm is warm-started and the number of iterations required to reach the solution is reduced. Starting from this point, the algorithm generates a series of boundary points that approaches the solution by projecting the proposed descent direction onto the feasible region. A numerical example is solved and a practical example in the simulation of rigid body dynamics is given to demonstrate the usage of the algorithm in solving such types of problem.
机译：介绍了一种正定线性互补问题的投影算法。该算法结合了梯度投影算法的基本思想。使用新的下降方向（称为中心向量）代替目标函数梯度的负值。该下降方向在整个迭代过程中保持固定，从而将搜索方向的计算量降低了每步O（n〜2）。该算法利用椭球算法在可行区域的边界上找到高级起点。因此，算法被热启动，并且减少了达到解决方案所需的迭代次数。从这一点开始，该算法生成一系列边界点，这些边界点通过将提出的下降方向投影到可行区域上来逼近解决方案。求解了一个数值示例，并给出了一个刚体动力学仿真的实际示例，以演示该算法在解决此类问题中的应用。

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