Herrich M. Local convergence of Newton-type methods for nonsmooth constrained equations and applications (Dresden, 2014). - ОГЛАВЛЕНИЕ / CONTENTS

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ОбложкаHerrich M. Local convergence of Newton-type methods for nonsmooth constrained equations and applications: Diss. … Dr. rer. nat. - Dresden: Technische Universität Dresden, 2014. - viii, 171 p. - Bibliogr.: p.163-170. 
 

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Оглавление / Contents
 
Notation ...................................................... vii
1  Introduction ................................................. 1
2  Preliminaries ................................................ 9
   2.1  Local Error Bound Condition ............................. 9
   2.2  Clarke's Generalized Jacobian .......................... 12
   2.3  Semismooth Functions ................................... 15
3  A Family of Newton-type Methods ............................. 17
   3.1  A General Framework .................................... 18
   3.2  A First Discussion of the Convergence Assumptions ...... 24
   3.3  Nonsmooth Inexact Newton Method ........................ 33
   3.4  LP-Newton Method ....................................... 39
   3.5  Constrained Levenberg-Marquardt Method ................. 46
4  Application to PC1-systems .................................. 61
   4.1  Discussion of the Convergence Assumptions .............. 63
        4.1.1  Assumption 1 .................................... 64
        4.1.2  Assumptions 2 and 3 ............................. 66
        4.1.3  Assumption 4 .................................... 74
        4.1.4  Sufficient Conditions for the Whole Set of 
               Assumptions 1-4 ................................. 81
   4.2  Reformulation with Slack Variables ..................... 88
   4.3  Application to Complementarity Systems ................ 101
5  Application to Special Problem Classes ..................... 107
   5.1  KKT Systems of Optimization Problems or Variational
        Inequalities .......................................... 108
   5.2  KKT Systems of GNEPs .................................. 121
   5.3  FJ Systems of GNEPs ................................... 130
6  A Hybrid Method for KKT Systems of GNEPs ................... 145
   6.1  Description and a Convergence Result .................. 146
   6.2  Discussion of Local Convergence ....................... 152
7  Conclusions and Outlook .................................... 159

Bibliography .................................................. 163


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