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  <doc>
    <id>935</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2006-08-01</completedDate>
    <publishedDate>2006-08-01</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A continuity result for Nemyckii Operators and some applications in PDE constrained optimal control</title>
    <abstract language="eng">This work explores two applications of a classical result on the continuity of Nemyckii operators to optimal control with PDEs. First, we present an alternative approach to the analysis of Newton's method for function space problems involving semi-smooth Nemyckii operators. A concise proof for superlinear convergence is presented, and sharpened bounds on the rate of convergence are derived. Second, we derive second order sufficient conditions for problems, where the underlying PDE has poor regularity properties. We point out that the analytical structure in both topics is essentially the same.</abstract>
    <identifier type="serial">06-41</identifier>
    <identifier type="opus3-id">935</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9354</identifier>
    <enrichment key="SourceTitle">A revised version appeared under the title: A Simplified Approach to Semismooth Newton Methods in Function Space in: SIAM J. Optimization, 19(3): 1417-1432, 2008</enrichment>
    <author>Anton Schiela</author>
    <series>
      <title>ZIB-Report</title>
      <number>06-41</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>continuity of Nemyckii Operators</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Newton methods in function space</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>second order sufficient conditions</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="46N40">Applications in numerical analysis [See also 65Jxx]</collection>
    <collection role="msc" number="49K20">Problems involving partial differential equations</collection>
    <collection role="msc" number="49M15">Newton-type methods</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/935/ZR-06-41.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/935/ZR-06-41.ps</file>
  </doc>
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