A nonsmooth version of the univariate optimization algorithm for locating the nearest extremum (locating extremum in nonsmooth univariate optimization)

Marek Smietanski

Open Mathematics (2008)

  • Volume: 6, Issue: 3, page 469-481
  • ISSN: 2391-5455

Abstract

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An algorithm for univariate optimization using a linear lower bounding function is extended to a nonsmooth case by using the generalized gradient instead of the derivative. A convergence theorem is proved under the condition of semismoothness. This approach gives a globally superlinear convergence of algorithm, which is a generalized Newton-type method.

How to cite

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Marek Smietanski. "A nonsmooth version of the univariate optimization algorithm for locating the nearest extremum (locating extremum in nonsmooth univariate optimization)." Open Mathematics 6.3 (2008): 469-481. <http://eudml.org/doc/269692>.

@article{MarekSmietanski2008,
abstract = {An algorithm for univariate optimization using a linear lower bounding function is extended to a nonsmooth case by using the generalized gradient instead of the derivative. A convergence theorem is proved under the condition of semismoothness. This approach gives a globally superlinear convergence of algorithm, which is a generalized Newton-type method.},
author = {Marek Smietanski},
journal = {Open Mathematics},
keywords = {univariate optimization; unconstrained optimization; linear bounding function; semismooth function; Univariate optimization; numerical examples; algorithm; superlinear convergence; Newton-type method},
language = {eng},
number = {3},
pages = {469-481},
title = {A nonsmooth version of the univariate optimization algorithm for locating the nearest extremum (locating extremum in nonsmooth univariate optimization)},
url = {http://eudml.org/doc/269692},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Marek Smietanski
TI - A nonsmooth version of the univariate optimization algorithm for locating the nearest extremum (locating extremum in nonsmooth univariate optimization)
JO - Open Mathematics
PY - 2008
VL - 6
IS - 3
SP - 469
EP - 481
AB - An algorithm for univariate optimization using a linear lower bounding function is extended to a nonsmooth case by using the generalized gradient instead of the derivative. A convergence theorem is proved under the condition of semismoothness. This approach gives a globally superlinear convergence of algorithm, which is a generalized Newton-type method.
LA - eng
KW - univariate optimization; unconstrained optimization; linear bounding function; semismooth function; Univariate optimization; numerical examples; algorithm; superlinear convergence; Newton-type method
UR - http://eudml.org/doc/269692
ER -

References

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