论文标题
迭代线性优化
Iterated Linear Optimization
论文作者
论文摘要
我们引入了一个固定点迭代过程，建立在紧凑型域上线性函数的优化之上。我们证明该过程始终收敛到固定点，并在各种凸集中探索固定点的集合。特别是，我们考虑椭圆形并得出其固定点的代数表征。我们证明椭圆的有吸引力的固定点正是其顶点。最后，我们讨论如何将固定点迭代用于四舍五入的半决赛编程松弛解决方案。
We introduce a fixed point iteration process built on optimization of a linear function over a compact domain. We prove the process always converges to a fixed point and explore the set of fixed points in various convex sets. In particular, we consider elliptopes and derive an algebraic characterization of their fixed points. We show that the attractive fixed points of an elliptope are exactly its vertices. Finally, we discuss how fixed point iteration can be used for rounding the solution of a semidefinite programming relaxation.
