Second-order algorithms for generalized finite and semi-infinite min-max problems

Elijah Polak; Liqun Qi; Defeng Sun

doi:10.1137/S1052623499358951

Second-order algorithms for generalized finite and semi-infinite min-max problems

Elijah Polak, Liqun Qi, Defeng Sun

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

3 Citations (Scopus)

Abstract

We present two second-order algorithms, one for solving a class of finite generalized min-max problems and one for solving semi-infinite generalized min-max problems. Our algorithms make use of optimality functions based on second-order approximations to the cost function and of corresponding search direction functions. Under reasonable assumptions we prove that both of these algorithms converge Q-superlinearly, with rate at least 3/2.

Original language	English
Pages (from-to)	937-961
Number of pages	25
Journal	SIAM Journal on Optimization
Volume	11
Issue number	4
DOIs	https://doi.org/10.1137/S1052623499358951
Publication status	Published - 1 Mar 2001

Keywords

Consistent approximations
Generalized min-max problems
Optimality functions
Second-order methods
Superlinear convergence

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

More information

10.1137/S1052623499358951

http://hdl.handle.net/10397/4758

Cite this

@article{ffc38d5f87014bf48af4e1a0f09c2e1a,

title = "Second-order algorithms for generalized finite and semi-infinite min-max problems",

abstract = "We present two second-order algorithms, one for solving a class of finite generalized min-max problems and one for solving semi-infinite generalized min-max problems. Our algorithms make use of optimality functions based on second-order approximations to the cost function and of corresponding search direction functions. Under reasonable assumptions we prove that both of these algorithms converge Q-superlinearly, with rate at least 3/2.",

keywords = "Consistent approximations, Generalized min-max problems, Optimality functions, Second-order methods, Superlinear convergence",

author = "Elijah Polak and Liqun Qi and Defeng Sun",

year = "2001",

month = mar,

day = "1",

doi = "10.1137/S1052623499358951",

language = "English",

volume = "11",

pages = "937--961",

journal = "SIAM Journal on Optimization",

issn = "1052-6234",

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

number = "4",

}

TY - JOUR

T1 - Second-order algorithms for generalized finite and semi-infinite min-max problems

AU - Polak, Elijah

AU - Qi, Liqun

AU - Sun, Defeng

PY - 2001/3/1

Y1 - 2001/3/1

N2 - We present two second-order algorithms, one for solving a class of finite generalized min-max problems and one for solving semi-infinite generalized min-max problems. Our algorithms make use of optimality functions based on second-order approximations to the cost function and of corresponding search direction functions. Under reasonable assumptions we prove that both of these algorithms converge Q-superlinearly, with rate at least 3/2.

AB - We present two second-order algorithms, one for solving a class of finite generalized min-max problems and one for solving semi-infinite generalized min-max problems. Our algorithms make use of optimality functions based on second-order approximations to the cost function and of corresponding search direction functions. Under reasonable assumptions we prove that both of these algorithms converge Q-superlinearly, with rate at least 3/2.

KW - Consistent approximations

KW - Generalized min-max problems

KW - Optimality functions

KW - Second-order methods

KW - Superlinear convergence

UR - http://www.scopus.com/inward/record.url?scp=0035602811&partnerID=8YFLogxK

U2 - 10.1137/S1052623499358951

DO - 10.1137/S1052623499358951

M3 - Journal article

SN - 1052-6234

VL - 11

SP - 937

EP - 961

JO - SIAM Journal on Optimization

JF - SIAM Journal on Optimization

IS - 4

ER -

Second-order algorithms for generalized finite and semi-infinite min-max problems

Abstract

Keywords

ASJC Scopus subject areas

More information

Other files and links

Fingerprint

Cite this