Local convergence of an inexact proximal algorithm for weakly convex functions
arXiv (Cornell University)(2023)
摘要
Since introduced by Martinet and Rockafellar, the proximal point algorithm was generalized in many fruitful directions. More recently, in 2002, Pennanen studied the proximal point algorithm without monotonicity. A year later, Iusem and Svaiter joined Pennanen to present inexact variants of the method, again without monotonicity. Building on the foundation laid by these two prior works, we propose a variant of the proximal point algorithm designed specifically for weakly convex functions. Our motivation for introducing this inexact algorithm is to increase its versatility and applicability in a broader range of scenarios in optimization and introduce a more adaptable version of the method for typical generalizations. Our study relies heavily on the Moreau envelope, a well-known mathematical tool used to analyze the behavior of the proximal operator. By leveraging the properties of the Moreau envelope, we are able to prove that the proximal algorithm converges in local contexts. Moreover, we present a complexity result to determine the practical feasibility of the proximal algorithm.
更多查看译文
关键词
inexact proximal algorithm,local convergence
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要