Projection algorithms with dynamic stepsize for constrained composite minimization

Volume 11, Issue 7, pp 927--936 http://dx.doi.org/10.22436/jnsa.011.07.05
Publication Date: May 24, 2018 Submission Date: December 25, 2017 Revision Date: April 13, 2018 Accteptance Date: April 14, 2018

Authors

Yujing Wu - Tianjin Vocational Institute, Tianjin 300410, P. R. China. Luoyi Shi - Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, P. R. China. Rudong Chen - Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, P. R. China.


Abstract

The problem of minimizing the sum of a large number of component functions over the intersection of a finite family of closed convex subsets of a Hilbert space is researched in the present paper. In the case of the number of the component functions is huge, the incremental projection methods are frequently used. Recently, we have proposed a new incremental gradient projection algorithm for this optimization problem. The new algorithm is parameterized by a single nonnegative constant \(\mu\). And the algorithm is proved to converge to an optimal solution if the dimensional of the Hilbert space is finite the step size is diminishing (such as \(\alpha_n=\mathcal{O}(1/n)\)). In this paper, the algorithm is modified by employing the constant and the dynamic stepsize, and the corresponding convergence properties are analyzed.


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