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Title: Globally convergent algorithms for finding zeros of duplomonotone mappings

We introduce a new class of mappings, called duplomonotone, which is strictly broader than the class of monotone mappings.We study some of themain 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.
Authors:
 [1] ;  [1]
  1. Univ. of Luxembourg (Luxembourg). Luxembourg Centre for Systems Biomedicine
Publication Date:
Grant/Contract Number:
SC0010429
Type:
Accepted Manuscript
Journal Name:
Optimization Letters
Additional Journal Information:
Journal Volume: 9; Journal Issue: 3; Journal ID: ISSN 1862-4472
Research Org:
Univ. du Luxembourg Etabl. Public (Luxembourg)
Sponsoring Org:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); Office of Science (SC), Biological and Environmental Research (BER) (SC-23)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Generalized monotonicity; Duplomonotone mapping; Monotone mapping; Global convergence; Line search method; Derivative-free algorithm; Biochemical reactions
OSTI Identifier:
1441135

Aragon Artacho, Francisco J., and Fleming, Ronan M. T.. Globally convergent algorithms for finding zeros of duplomonotone mappings. United States: N. p., Web. doi:10.1007/s11590-014-0769-z.
Aragon Artacho, Francisco J., & Fleming, Ronan M. T.. Globally convergent algorithms for finding zeros of duplomonotone mappings. United States. doi:10.1007/s11590-014-0769-z.
Aragon Artacho, Francisco J., and Fleming, Ronan M. T.. 2014. "Globally convergent algorithms for finding zeros of duplomonotone mappings". United States. doi:10.1007/s11590-014-0769-z. https://www.osti.gov/servlets/purl/1441135.
@article{osti_1441135,
title = {Globally convergent algorithms for finding zeros of duplomonotone mappings},
author = {Aragon Artacho, Francisco J. and Fleming, Ronan M. T.},
abstractNote = {We introduce a new class of mappings, called duplomonotone, which is strictly broader than the class of monotone mappings.We study some of themain 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.},
doi = {10.1007/s11590-014-0769-z},
journal = {Optimization Letters},
number = 3,
volume = 9,
place = {United States},
year = {2014},
month = {9}
}