A note on the convergence of an inertial version of a diagonal hybrid projection-point algorithm.

Miguel Carrasco; Karine Pichard

doi:10.1080/02331930801951389

A note on the convergence of an inertial version of a diagonal hybrid projection-point algorithm.

Miguel Carrasco^*, Karine Pichard

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this note, an inertial and relaxed version of a diagonal hybrid projectionproximal point algorithm is considered, in order to find the minimum of a function f approximated by a sequence of functions (in general, smoother than f or taking into account some constraints of the problem). Two convergence theorems are proved under different kind of assumptions, which allows to apply the method in various cases.

Original language	English
Pages (from-to)	561-574
Number of pages	14
Journal	Optimization
Volume	59
Issue number	4
DOIs	https://doi.org/10.1080/02331930801951389
State	Published - May 2010

Bibliographical note

Funding Information:
M. Carrasco was partially supported by FONDECYT grant 3080037. K. Pichard was supported by ECOS/CONICYT. The authors wish to thank the Centro de Modelamiento Matemático where part of this research was carried out.

Keywords

Diagonal iteration
Global convergence
Hybrid method
Inertial term
Parametric approximation
Proximal point
Relaxation

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10.1080/02331930801951389

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title = "A note on the convergence of an inertial version of a diagonal hybrid projection-point algorithm.",

abstract = "In this note, an inertial and relaxed version of a diagonal hybrid projectionproximal point algorithm is considered, in order to find the minimum of a function f approximated by a sequence of functions (in general, smoother than f or taking into account some constraints of the problem). Two convergence theorems are proved under different kind of assumptions, which allows to apply the method in various cases.",

keywords = "Diagonal iteration, Global convergence, Hybrid method, Inertial term, Parametric approximation, Proximal point, Relaxation",

author = "Miguel Carrasco and Karine Pichard",

note = "Funding Information: M. Carrasco was partially supported by FONDECYT grant 3080037. K. Pichard was supported by ECOS/CONICYT. The authors wish to thank the Centro de Modelamiento Matem{\'a}tico where part of this research was carried out.",

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T1 - A note on the convergence of an inertial version of a diagonal hybrid projection-point algorithm.

AU - Carrasco, Miguel

AU - Pichard, Karine

N1 - Funding Information: M. Carrasco was partially supported by FONDECYT grant 3080037. K. Pichard was supported by ECOS/CONICYT. The authors wish to thank the Centro de Modelamiento Matemático where part of this research was carried out.

PY - 2010/5

Y1 - 2010/5

N2 - In this note, an inertial and relaxed version of a diagonal hybrid projectionproximal point algorithm is considered, in order to find the minimum of a function f approximated by a sequence of functions (in general, smoother than f or taking into account some constraints of the problem). Two convergence theorems are proved under different kind of assumptions, which allows to apply the method in various cases.

AB - In this note, an inertial and relaxed version of a diagonal hybrid projectionproximal point algorithm is considered, in order to find the minimum of a function f approximated by a sequence of functions (in general, smoother than f or taking into account some constraints of the problem). Two convergence theorems are proved under different kind of assumptions, which allows to apply the method in various cases.

KW - Diagonal iteration

KW - Global convergence

KW - Hybrid method

KW - Inertial term

KW - Parametric approximation

KW - Proximal point

KW - Relaxation

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DO - 10.1080/02331930801951389

M3 - Article

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VL - 59

SP - 561

EP - 574

JO - Optimization

JF - Optimization

IS - 4

ER -

A note on the convergence of an inertial version of a diagonal hybrid projection-point algorithm.

Abstract

Bibliographical note

Keywords

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