Finite Termination of Inexact Proximal Point Algorithms in Hilbert Spaces

作者：Wang, J. H.^*; Li, C.; Yao, J. -C.

来源：Journal of Optimization Theory and Applications, 2015, 166(1): 188-212.

DOI：10.1007/s10957-014-0689-1

• Finite termination
• Inexact proximal point algorithms
• Maximal monotone
• Projected gradient method

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 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.

• 出版日期2015-7
• 单位浙江大学; 浙江工业大学