具有自适应离散的巴拿赫空间中的“FISTA“
"FISTA" in Banach spaces with adaptive discretisations
摘要：
FISTA是一种流行的凸优化算法，已知只要极小值包含在合适的希尔伯特空间中，该算法就以最优速率收敛。我们提出了一个修改后的算法，其中每次迭代是在一个子集，允许在每次迭代改变。提供了保证收敛的充分条件，尽管根据具体问题的条件而降低速度。这些条件有一个自然的解释时，极小存在于一个潜在的巴拿赫空间。典型的例子是L1处罚重建，我们提供详细的理论和数值分析。
英文摘要：
FISTA is a popular convex optimisation algorithm which is known to converge at an optimal rate whenever a minimiser is contained in a suitable Hilbert space. We propose a modified algorithm where each iteration is performed in a subset which is allowed to change at every iteration. Sufficient conditions are provided for guaranteed convergence, although at a reduced rate depending on the conditioning of the specific problem. These conditions have a natural interpretation when a minimiser exists in an underlying Banach space. Typical examples are L1-penalised reconstructions where we provide detailed theoretical and numerical analysis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
