论文标题
投射到半空间和超平面的交叉点上
Projecting onto intersections of halfspaces and hyperplanes
论文作者
论文摘要
众所周知，当关闭相应的线性子空间的总和时，投影组成的迭代序列将封闭仿射子空间的迭代序列线性收敛至仿射子空间的相交。在这项工作的启发下，我们系统地研究了投射到半空间和超平面相交的投影之间的关系，以及投影在半空间和超平面上的组成。此外，作为副产品，我们提供了Karush-kuhn-tucker条件，以表征希尔伯特空间中有限的许多平等和不平等约束的凸优化的最佳解决方案，并构建了针对超飞机和半空间相交的投影的明确公式。
It is well-known that the sequence of iterations of the composition of projections onto closed affine subspaces converges linearly to the projection onto the intersection of the affine subspaces when the sum of the corresponding linear subspaces is closed. Inspired by this, in this work, we systematically study the relation between the projection onto intersection of halfspaces and hyperplanes, and the composition of projections onto halfspaces and hyperplanes. In addition, as by-products, we provide the Karush-Kuhn-Tucker conditions for characterizing the optimal solution of convex optimization with finitely many equality and inequality constraints in Hilbert spaces and construct an explicit formula for the projection onto the intersection of hyperplane and halfspace.
