Monotone operator and the inexact entropic proximal point algorithm

2019 ◽  
Vol 13 (6) ◽  
pp. 247-258
Author(s):  
S. Kabbadj
Keyword(s):  
Monotone Operator ◽  
Proximal Point Algorithm ◽  
Proximal Point

scholarly journals A Modified Regularization Method for the Proximal Point Algorithm

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Shuang Wang
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Monotone Operator ◽  
Maximal Monotone Operator ◽  
Regularization Method ◽  
Proximal Point Algorithm ◽  
Maximal Monotone ◽  
Proximal Point ◽  
Weaker Conditions

Under some weaker conditions, we prove the strong convergence of the sequence generated by a modified regularization method of finding a zero for a maximal monotone operator in a Hilbert space. In addition, an example is also given in order to illustrate the effectiveness of our generalizations. The results presented in this paper can be viewed as the improvement, supplement, and extension of the corresponding results.

MONOTONE OPERATORS AND THE PROXIMAL POINT ALGORITHM IN COMPLETE CAT(0) METRIC SPACES

2016 ◽  
Vol 103 (1) ◽  
pp. 70-90 ◽  
Author(s):  
HADI KHATIBZADEH ◽  
SAJAD RANJBAR
Keyword(s):  
Strong Convergence ◽  
Monotone Operator ◽  
Proximal Point Algorithm ◽  
Metric Spaces ◽  
Monotone Operators ◽  
Proximal Point ◽  
Range Condition ◽  
Special Cases ◽  
Inexact Proximal

In this paper, we generalize monotone operators, their resolvents and the proximal point algorithm to complete CAT(0) spaces. We study some properties of monotone operators and their resolvents. We show that the sequence generated by the inexact proximal point algorithm $\unicode[STIX]{x1D6E5}$-converges to a zero of the monotone operator in complete CAT(0) spaces. A strong convergence (convergence in metric) result is also presented. Finally, we consider two important special cases of monotone operators and we prove that they satisfy the range condition (see Section 4 for the definition), which guarantees the existence of the sequence generated by the proximal point algorithm.

STRONG AND Δ - CONVERGENCE THEOREMS USING MODIFIED PROXIMAL POINT ALGORITHM IN CAT(0) SPACES

2018 ◽  
Vol 7 (2) ◽  
pp. 8
Author(s):  
KUMAR DAS APURVA ◽  
DHAR DIWAN SHAILESH ◽  
DASHPUTRE SAMIR ◽  
◽  
◽  
...  
Keyword(s):  
Proximal Point Algorithm ◽  
Proximal Point ◽  
Convergence Theorems
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