A proximal iterative approach to a non-convex optimization problem

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• 作者：A. Moudafi
• 关键词：Optimization ; Prox-regularity ; Krasnosel&#x2019 ; skii&#x2013 ; Mann algorithm ; Fixed-point
• 刊名：Nonlinear Analysis
• 出版年：2010
• 出版时间：15 January 2010
• 年：2010
• 卷：72
• 期：2
• 页码：704-709
• 全文大小：400 K

文摘

We consider a variable Krasnosel’skii–Mann algorithm for approximating critical points of a prox-regular function or equivalently for finding fixed-points of its proximal mapping prox_λf. The novelty of our approach is that the latter is not non-expansive any longer. We prove that the sequence generated by such algorithm (via the formula x_k+1=(1−α_k)x_k+α_kprox_λkfx_k, where (α_k) is a sequence in (0,1)), is an approximate fixed-point of the proximal mapping and converges provided that the function under consideration satisfies a local metric regularity condition.