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

82 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

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10.1137/S1052623494278839

Cite this

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AU - Qi, Liqun

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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 - https://www.scopus.com/pages/publications/0030508716

U2 - 10.1137/S1052623494278839

DO - 10.1137/S1052623494278839

M3 - Journal article

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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

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