# Generalized Newton and NCP-methods: convergence, regularity, actions

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2000)

- Volume: 20, Issue: 2, page 209-244
- ISSN: 1509-9407

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topBernd Kummer. "Generalized Newton and NCP-methods: convergence, regularity, actions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 20.2 (2000): 209-244. <http://eudml.org/doc/271515>.

@article{BerndKummer2000,

abstract = {Solutions of several problems can be modelled as solutions of nonsmooth equations. Then, Newton-type methods for solving such equations induce particular iteration steps (actions) and regularity requirements in the original problems. We study these actions and requirements for nonlinear complementarity problems (NCP's) and Karush-Kuhn-Tucker systems (KKT) of optimization models. We demonstrate their dependence on the applied Newton techniques and the corresponding reformulations. In this way, connections to SQP-methods, to penalty-barrier methods and to general properties of so-called NCP-functions are shown. Moreover, direct comparisons of the hypotheses and actions in terms of the original problems become possible. Besides, we point out the possibilities and bounds of such methods in dependence of smoothness.},

author = {Bernd Kummer},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {nonsmooth functions; generalized Newton methods; critical points; complementarity; SQP methods; inverse mappings; regularity; nonlinear complementarity problems; nonsmooth equations; Newton-type methods; Karush-Kuhn-Tucker systems; SQP-methods; penalty-barrier methods; NCP-functions; dependence of smoothness},

language = {eng},

number = {2},

pages = {209-244},

title = {Generalized Newton and NCP-methods: convergence, regularity, actions},

url = {http://eudml.org/doc/271515},

volume = {20},

year = {2000},

}

TY - JOUR

AU - Bernd Kummer

TI - Generalized Newton and NCP-methods: convergence, regularity, actions

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2000

VL - 20

IS - 2

SP - 209

EP - 244

AB - Solutions of several problems can be modelled as solutions of nonsmooth equations. Then, Newton-type methods for solving such equations induce particular iteration steps (actions) and regularity requirements in the original problems. We study these actions and requirements for nonlinear complementarity problems (NCP's) and Karush-Kuhn-Tucker systems (KKT) of optimization models. We demonstrate their dependence on the applied Newton techniques and the corresponding reformulations. In this way, connections to SQP-methods, to penalty-barrier methods and to general properties of so-called NCP-functions are shown. Moreover, direct comparisons of the hypotheses and actions in terms of the original problems become possible. Besides, we point out the possibilities and bounds of such methods in dependence of smoothness.

LA - eng

KW - nonsmooth functions; generalized Newton methods; critical points; complementarity; SQP methods; inverse mappings; regularity; nonlinear complementarity problems; nonsmooth equations; Newton-type methods; Karush-Kuhn-Tucker systems; SQP-methods; penalty-barrier methods; NCP-functions; dependence of smoothness

UR - http://eudml.org/doc/271515

ER -

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