论文标题
凸优化中无处不在的算法生成自缩序列
Ubiquitous algorithms in convex optimization generate self-contracted sequences
论文作者
论文摘要
在这项工作中，我们表明，各种算法在凸优化中无处不在（例如，近端梯度，交替的投影和平均投影）生成自缩的序列$ \ {x_ {x_ {k} \} _ {k \ in \ in \ nathbb {n}} $。结果，可以授予针对\ emph {length}（$ \ sum_ {k \ ge 0} \ vert x_ {k+1} -x_k \ vert $）的小说通用绑定。此外，该结合与问题的具体数据（集合，函数）以及所涉及的步骤尺寸无关，仅取决于空间的维度。
In this work we show that various algorithms, ubiquitous in convex optimization (e.g. proximal-gradient, alternating projections and averaged projections) generate self-contracted sequences $\{x_{k}\}_{k\in\mathbb{N}}$. As a consequence, a novel universal bound for the \emph{length} ($\sum_{k\ge 0}\Vert x_{k+1}-x_k\Vert$) can be deduced. In addition, this bound is independent of both the concrete data of the problem (sets, functions) as well as the stepsize involved, and only depends on the dimension of the space.
