用Picard方法投影到单纯锥上
Projection onto simplicial cones by Picard's method
摘要：
利用Moreau的投影到锥上的分解定理，将投影到单纯锥上的问题归结为求非光滑方程组的唯一解。它表明，皮卡德的方法适用于方程组的问题，投影到一个单纯锥产生一个序列，线性收敛到系统的解决方案。数值实验比较了Picard法和半光滑牛顿法求解点投影到单纯锥上的非光滑方程组的结果。
英文摘要：
By using Moreau's decomposition theorem for projecting onto cones, the problem of projecting onto a simplicial cone is reduced to finding the unique solution of a nonsmooth system of equations. It is shown that Picard's method applied to the system of equations associated to the problem of projecting onto a simplicial cone generates a sequence that converges linearly to the solution of the system. Numerical experiments are presented making the comparison between Picard's and semi-smooth Newton's methods to solve the nonsmooth system associated with the problem of projecting a point onto a simplicial cone.
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