An Accelerated Inexact Proximal Point Algorithm for Convex Minimization

The proximal point algorithm is classical and popular in the community of optimization. In practice, inexact proximal point algorithms which solve the involved proximal subproblems approximately subject to certain inexact criteria are truly implementable. In this paper, we first propose an inexact p...

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Veröffentlicht in:Journal of optimization theory and applications Jg. 154; H. 2; S. 536 - 548
Hauptverfasser: He, Bingsheng, Yuan, Xiaoming
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.08.2012
Springer Nature B.V
Schlagworte:
Acceleration
Accuracy
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Studies
Theory of Computation
Convex minimization
Inexact
Proximal point algorithm
Acceleration
ISSN:0022-3239, 1573-2878
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Zusammenfassung:The proximal point algorithm is classical and popular in the community of optimization. In practice, inexact proximal point algorithms which solve the involved proximal subproblems approximately subject to certain inexact criteria are truly implementable. In this paper, we first propose an inexact proximal point algorithm with a new inexact criterion for solving convex minimization, and show its O (1/ k ) iteration-complexity. Then we show that this inexact proximal point algorithm is eligible for being accelerated by some influential acceleration schemes proposed by Nesterov. Accordingly, an accelerated inexact proximal point algorithm with an iteration-complexity of O (1/ k 2 ) is proposed.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-011-9948-6