Convergence analysis of a proximal point algorithm for minimizing differences of functions

Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A significant progress to go beyond convexity was made by considering the class of functions representable as differences...

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Bibliographic Details
Published in:Optimization Vol. 66; no. 1; pp. 129 - 147
Main Authors: An, Nguyen Thai, Nam, Nguyen Mau
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis 02.01.2017
Taylor & Francis LLC
Subjects:
Algorithms
Computational geometry
Convergence
Convex analysis
Convexity
DC programming
difference of convex functions
Kurdyka-ᴌojasiewicz inequality
Mathematical analysis
Mathematical models
Numerical analysis
Optimization
proximal point algorithm
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Summary:Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A significant progress to go beyond convexity was made by considering the class of functions representable as differences of convex functions. In this paper, we introduce a generalized proximal point algorithm to minimize the difference of a nonconvex function and a convex function. We also study convergence results of this algorithm under the main assumption that the objective function satisfies the Kurdyka-ᴌojasiewicz property.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2016.1253694