Quasi-Newton bundle-type methods for nondifferentiable convex optimization

Robert Mifflin; Defeng Sun; Liqun Qi

doi:10.1137/S1052623496303329

Quasi-Newton bundle-type methods for nondifferentiable convex optimization

Robert Mifflin, Defeng Sun, Liqun Qi

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

38 Citations (Scopus)

Abstract

In this paper we provide implementable methods for solving nondifferentiable convex optimization problems. A typical method minimizes an approximate Moreau-Yosida regularization using a quasi-Newton technique with inexact function and gradient values which are generated by a finite inner bundle algorithm. For a BFGS bundle-type method global and superlinear convergence results for the outer iteration sequence are obtained.

Original language	English
Pages (from-to)	583-603
Number of pages	21
Journal	SIAM Journal on Optimization
Volume	8
Issue number	2
DOIs	https://doi.org/10.1137/S1052623496303329
Publication status	Published - 1 Jan 1998
Externally published	Yes

Keywords

Bundle method
Moreau-Yosida regularization
Quasi-Newton method
Superlinear convergence

ASJC Scopus subject areas

Software
Theoretical Computer Science

More information

10.1137/S1052623496303329

Cite this

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AU - Qi, Liqun

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AB - In this paper we provide implementable methods for solving nondifferentiable convex optimization problems. A typical method minimizes an approximate Moreau-Yosida regularization using a quasi-Newton technique with inexact function and gradient values which are generated by a finite inner bundle algorithm. For a BFGS bundle-type method global and superlinear convergence results for the outer iteration sequence are obtained.

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KW - Moreau-Yosida regularization

KW - Quasi-Newton method

KW - Superlinear convergence

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Quasi-Newton bundle-type methods for nondifferentiable convex optimization

Abstract

Keywords

ASJC Scopus subject areas

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