Finite Termination of Inexact Proximal Point Algorithms in Hilbert Spaces

J. H. Wang (), C. Li () and J.-C. Yao ()
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J. H. Wang: Zhejiang University of Technology
C. Li: Zhejiang University
J.-C. Yao: Kaohsiung Medical University

Journal of Optimization Theory and Applications, 2015, vol. 166, issue 1, No 9, 188-212

Abstract: Abstract In the present paper, we study the finite termination of sequences generated by inexact proximal point algorithms for finding zeroes of a maximal monotone (set-valued) operator $$T$$ T on a Hilbert space. Under some mild conditions, we get that a sequence generated by inexact proximal point algorithm stops after a finite number of iterations. Our results extend the corresponding results in Rockafellar (SIAM J Control Optim 14:877–898, 1976). In particular, for optimization problems, our results improve corresponding results in Ferris (Math Progr 50:359–366, 1991). As applications, we obtain finite termination of projected gradient method.

Keywords: Finite termination; Inexact proximal point algorithms; Maximal monotone; Projected gradient method; 49J53; 47H04; 65K10 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10957-014-0689-1

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