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

Open Mathematics (2008)

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

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topMarek 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 -

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