【摘要】 提出求解单调线性权互补问题(WLCP)的全牛顿步可行内点算法。基于线性优化的连续可微函数，给出中心方程的新等价形式，接着运用牛顿法求解定义中心路径的等价方程组，从而得到单调WLCP的新搜索方向。沿该搜索方向使用全牛顿步，无需进行线搜索。通过适当选取参数，分析了全牛顿步的严格可行性，证得算法是二次收敛的且具有多项式时间迭代复杂度。最后数值实验结果表明算法有效。更多还原

【Abstract】 A full-Newton step feasible interior-point method was proposed to solve the monotone weighted linear complementarity problem(WLCP).Based on continuously differentiable function for linear optimization, new equivalent form of the central equation was given.Then Newton’s method was applied to the equivalent system of equations defining the central path, which leads to new search direction for the monotone WLCP.Full-Newton steps are used along this search direction, and hence no line search was required.By appropriately selecting parameters, the strict feasibility of the full-Newton step was analyzed.It was proved that the algorithm was quadratically convergent and has polynomial time iteration complexity.Some numerical results showed that the algorithm was effective.更多还原