A descent algorithm for nonsmooth convex optimization

This paper presents a new descent algorithm for minimizing a convex function which is not necessarily differentiable. The algorithm can be implemented and may be considered a modification of the epsilon -subgradient algorithm and Lemarechal's descent algorithm. Also our algorithm is seen to be...

Full description

Saved in:
Bibliographic Details
Published inMathematical programming Vol. 30; no. 2; pp. 163 - 175
Main Author Fukushima, Masao
Format Journal Article
LanguageEnglish
Published Heidelberg Springer 01.10.1984
Subjects
Applied sciences
Exact sciences and technology
Mathematical programming
Operational research and scientific management
Operational research. Management science
Convex function
Function minimization
Algorithm
Convex programming
Descent method
Mathematical programming
Online AccessGet full text
ISSN0025-5610
1436-4646
DOI10.1007/BF02591883

Cover

More Information
Summary:This paper presents a new descent algorithm for minimizing a convex function which is not necessarily differentiable. The algorithm can be implemented and may be considered a modification of the epsilon -subgradient algorithm and Lemarechal's descent algorithm. Also our algorithm is seen to be closely related to the proximal point algorithm applied to convex minimization problems. A convergence theorem for the algorithms is established under the assumption that the objective function is bounded from below. Limited computational experience with the algorithm is also reported.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0025-5610
1436-4646
DOI:10.1007/BF02591883