A smoothing trust region filter algorithm for nonsmooth least squares problems

Xiaojun Chen; Shou Qiang Du; Yang Zhou

doi:10.1007/s11425-015-5116-z

A smoothing trust region filter algorithm for nonsmooth least squares problems

Xiaojun Chen
, Shou Qiang Du
, Yang Zhou

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

5 Citations (Scopus)

Abstract

We propose a smoothing trust region filter algorithm for nonsmooth nonconvex least squares problems. We present convergence theorems of the proposed algorithm to a Clarke stationary point or a global minimizer of the objective function under certain conditions. Preliminary numerical experiments show the efficiency of the proposed algorithm for finding zeros of a system of polynomial equations with high degrees on the sphere and solving differential variational inequalities.

Original language	English
Pages (from-to)	999-1014
Number of pages	16
Journal	Science China Mathematics
Volume	59
Issue number	5
DOIs	https://doi.org/10.1007/s11425-015-5116-z
Publication status	Published - 1 May 2016

Keywords

filter technique
smoothing approximation
trust region method

ASJC Scopus subject areas

General Mathematics

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10.1007/s11425-015-5116-z

Cite this

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title = "A smoothing trust region filter algorithm for nonsmooth least squares problems",

abstract = "We propose a smoothing trust region filter algorithm for nonsmooth nonconvex least squares problems. We present convergence theorems of the proposed algorithm to a Clarke stationary point or a global minimizer of the objective function under certain conditions. Preliminary numerical experiments show the efficiency of the proposed algorithm for finding zeros of a system of polynomial equations with high degrees on the sphere and solving differential variational inequalities.",

keywords = "filter technique, smoothing approximation, trust region method",

author = "Xiaojun Chen and Du, \{Shou Qiang\} and Yang Zhou",

year = "2016",

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T1 - A smoothing trust region filter algorithm for nonsmooth least squares problems

AU - Chen, Xiaojun

AU - Du, Shou Qiang

AU - Zhou, Yang

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N2 - We propose a smoothing trust region filter algorithm for nonsmooth nonconvex least squares problems. We present convergence theorems of the proposed algorithm to a Clarke stationary point or a global minimizer of the objective function under certain conditions. Preliminary numerical experiments show the efficiency of the proposed algorithm for finding zeros of a system of polynomial equations with high degrees on the sphere and solving differential variational inequalities.

AB - We propose a smoothing trust region filter algorithm for nonsmooth nonconvex least squares problems. We present convergence theorems of the proposed algorithm to a Clarke stationary point or a global minimizer of the objective function under certain conditions. Preliminary numerical experiments show the efficiency of the proposed algorithm for finding zeros of a system of polynomial equations with high degrees on the sphere and solving differential variational inequalities.

KW - filter technique

KW - smoothing approximation

KW - trust region method

UR - https://www.scopus.com/pages/publications/84953341263

U2 - 10.1007/s11425-015-5116-z

DO - 10.1007/s11425-015-5116-z

M3 - Journal article

SN - 1674-7283

VL - 59

SP - 999

EP - 1014

JO - Science China Mathematics

JF - Science China Mathematics

IS - 5

ER -

A smoothing trust region filter algorithm for nonsmooth least squares problems

Abstract

Keywords

ASJC Scopus subject areas

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