论文标题
无限尺寸凸优化问题的单预测程序
Single-Projection Procedure for Infinite Dimensional Convex Optimization Problems
论文作者
论文摘要
在这项工作中，我们考虑了真正的希尔伯特空间中的一类凸优化问题，可以通过执行单个投影（即，通过将一个不可行的点投射到可行的集合中）来解决。我们的结果改善了Nurminski（2015）中的线性编程设置建立的结果：（i）可能具有多种解决方案，（ii）不满足严格的互补条件，并且（iii）具有非线性凸的约束。作为我们分析的副产品，我们对不可行点和可行集合之间所需距离的定量估计值进行定量估计，以便其投影成为问题的解决方案。我们的分析依赖于约束集的“清晰度”属性；我们在这里介绍的新属性。
In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those established for the linear programming setting in Nurminski (2015) by considering problems that: (i) may have multiple solutions, (ii) do not satisfy strict complementary conditions, and (iii) possess non-linear convex constraints. As a by-product of our analysis, we provide a quantitative estimate on the required distance between the infeasible point and the feasible set in order for its projection to be a solution of the problem. Our analysis relies on a "sharpness" property of the constraint set; a new property we introduce here.
