A globally and superlinearly convergent algorithm for nonsmooth convex minimization

Masao Fukushima; Liqun Qi

doi:10.1137/S1052623494278839

A globally and superlinearly convergent algorithm for nonsmooth convex minimization

Masao Fukushima, Liqun Qi

Research output: Journal article publication › Journal article › Academic research › peer-review

77 Citations (Scopus)

Abstract

It is well known that a possibly nondifferentiable convex minimization problem can be transformed into a differentiable convex minimization problem by way of the Moreau-Yosida regularization. This paper presents a globally convergent algorithm that is designed to solve the latter problem. Under additional semismoothness and regularity assumptions, the proposed algorithm is shown to have a Q-superlinear rate of convergence.

Original language	English
Pages (from-to)	1106-1120
Number of pages	15
Journal	SIAM Journal on Optimization
Volume	6
Issue number	4
DOIs	https://doi.org/10.1137/S1052623494278839
Publication status	Published - 1 Jan 1996
Externally published	Yes

Keywords

Global convergence
Moreau-Yosida regularization
Nonsmooth convex optimization
Semismoothness
Superlinear convergence

ASJC Scopus subject areas

Software
Theoretical Computer Science

More information

10.1137/S1052623494278839

Cite this

@article{68323baf5fba4ee2b56f4c4b3fc5cb4e,

title = "A globally and superlinearly convergent algorithm for nonsmooth convex minimization",

abstract = "It is well known that a possibly nondifferentiable convex minimization problem can be transformed into a differentiable convex minimization problem by way of the Moreau-Yosida regularization. This paper presents a globally convergent algorithm that is designed to solve the latter problem. Under additional semismoothness and regularity assumptions, the proposed algorithm is shown to have a Q-superlinear rate of convergence.",

keywords = "Global convergence, Moreau-Yosida regularization, Nonsmooth convex optimization, Semismoothness, Superlinear convergence",

author = "Masao Fukushima and Liqun Qi",

year = "1996",

month = jan,

day = "1",

doi = "10.1137/S1052623494278839",

language = "English",

volume = "6",

pages = "1106--1120",

journal = "SIAM Journal on Optimization",

issn = "1052-6234",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "4",

}

TY - JOUR

T1 - A globally and superlinearly convergent algorithm for nonsmooth convex minimization

AU - Fukushima, Masao

AU - Qi, Liqun

PY - 1996/1/1

Y1 - 1996/1/1

N2 - It is well known that a possibly nondifferentiable convex minimization problem can be transformed into a differentiable convex minimization problem by way of the Moreau-Yosida regularization. This paper presents a globally convergent algorithm that is designed to solve the latter problem. Under additional semismoothness and regularity assumptions, the proposed algorithm is shown to have a Q-superlinear rate of convergence.

AB - It is well known that a possibly nondifferentiable convex minimization problem can be transformed into a differentiable convex minimization problem by way of the Moreau-Yosida regularization. This paper presents a globally convergent algorithm that is designed to solve the latter problem. Under additional semismoothness and regularity assumptions, the proposed algorithm is shown to have a Q-superlinear rate of convergence.

KW - Global convergence

KW - Moreau-Yosida regularization

KW - Nonsmooth convex optimization

KW - Semismoothness

KW - Superlinear convergence

UR - http://www.scopus.com/inward/record.url?scp=0030508716&partnerID=8YFLogxK

U2 - 10.1137/S1052623494278839

DO - 10.1137/S1052623494278839

M3 - Journal article

SN - 1052-6234

VL - 6

SP - 1106

EP - 1120

JO - SIAM Journal on Optimization

JF - SIAM Journal on Optimization

IS - 4

ER -

A globally and superlinearly convergent algorithm for nonsmooth convex minimization

Abstract

Keywords

ASJC Scopus subject areas

More information

Other files and links

Fingerprint

Cite this