Globally convergent algorithms for finding zeros of duplomonotone mappings

Francisco J. Aragón Artacho; Ronan M.T. Fleming

doi:10.1007/s11590-014-0769-z

Globally convergent algorithms for finding zeros of duplomonotone mappings

Francisco J. Aragón Artacho
, Ronan M.T. Fleming

University of Luxembourg

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

4 Citations (Scopus)

Abstract

We introduce a new class of mappings, called duplomonotone, which is strictly broader than the class of monotone mappings. We study some of the main properties of duplomonotone functions and provide various examples, including nonlinear duplomonotone functions arising from the study of systems of biochemical reactions. Finally, we present three variations of a derivative-free line search algorithm for finding zeros of systems of duplomonotone equations, and we prove their linear convergence to a zero of the function.

Original language	English
Pages (from-to)	569-584
Number of pages	16
Journal	Optimization Letters
Volume	9
Issue number	3
DOIs	https://doi.org/10.1007/s11590-014-0769-z
Publication status	Published - Mar 2015
Externally published	Yes

Keywords

Biochemical reactions
Derivative-free algorithm
Duplomonotone mapping
Generalized monotonicity
Global convergence
Line search method
Monotone mapping

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10.1007/s11590-014-0769-z

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title = "Globally convergent algorithms for finding zeros of duplomonotone mappings",

abstract = "We introduce a new class of mappings, called duplomonotone, which is strictly broader than the class of monotone mappings. We study some of the main properties of duplomonotone functions and provide various examples, including nonlinear duplomonotone functions arising from the study of systems of biochemical reactions. Finally, we present three variations of a derivative-free line search algorithm for finding zeros of systems of duplomonotone equations, and we prove their linear convergence to a zero of the function.",

keywords = "Biochemical reactions, Derivative-free algorithm, Duplomonotone mapping, Generalized monotonicity, Global convergence, Line search method, Monotone mapping",

author = "\{Arag{\'o}n Artacho\}, \{Francisco J.\} and Fleming, \{Ronan M.T.\}",

note = "Publisher Copyright: {\textcopyright} 2014, The Author(s).",

year = "2015",

month = mar,

doi = "10.1007/s11590-014-0769-z",

language = "English",

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T1 - Globally convergent algorithms for finding zeros of duplomonotone mappings

AU - Aragón Artacho, Francisco J.

AU - Fleming, Ronan M.T.

PY - 2015/3

Y1 - 2015/3

N2 - We introduce a new class of mappings, called duplomonotone, which is strictly broader than the class of monotone mappings. We study some of the main properties of duplomonotone functions and provide various examples, including nonlinear duplomonotone functions arising from the study of systems of biochemical reactions. Finally, we present three variations of a derivative-free line search algorithm for finding zeros of systems of duplomonotone equations, and we prove their linear convergence to a zero of the function.

AB - We introduce a new class of mappings, called duplomonotone, which is strictly broader than the class of monotone mappings. We study some of the main properties of duplomonotone functions and provide various examples, including nonlinear duplomonotone functions arising from the study of systems of biochemical reactions. Finally, we present three variations of a derivative-free line search algorithm for finding zeros of systems of duplomonotone equations, and we prove their linear convergence to a zero of the function.

KW - Biochemical reactions

KW - Derivative-free algorithm

KW - Duplomonotone mapping

KW - Generalized monotonicity

KW - Global convergence

KW - Line search method

KW - Monotone mapping

UR - https://www.scopus.com/pages/publications/84923811687

U2 - 10.1007/s11590-014-0769-z

DO - 10.1007/s11590-014-0769-z

M3 - Article

SN - 1862-4472

VL - 9

SP - 569

EP - 584

JO - Optimization Letters

JF - Optimization Letters

IS - 3

ER -

Globally convergent algorithms for finding zeros of duplomonotone mappings

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Keywords

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