1 Ocak 2014 Dergi makalesi Açık Erişim

Mengi, Emre; Yildirim, E. Alper; Kilic, Mustafa

MARC21 XML

<?xml version='1.0' encoding='UTF-8'?>
<record xmlns="http://www.loc.gov/MARC21/slim">
  <leader>00000nam##2200000uu#4500</leader>
  <datafield tag="909" ind1="C" ind2="O">
    <subfield code="p">user-tubitak-destekli-proje-yayinlari</subfield>
    <subfield code="o">oai:zenodo.org:66919</subfield>
  </datafield>
  <datafield tag="520" ind1=" " ind2=" ">
    <subfield code="a">This work concerns the global minimization of a prescribed eigenvalue or a weighted sum of prescribed eigenvalues of a Hermitian matrix-valued function depending on its parameters analytically in a box. We describe how the analytical properties of eigenvalue functions can be put into use to derive piecewise quadratic functions that underestimate the eigenvalue functions. These piecewise quadratic underestimators lead us to a global minimization algorithm, originally due to Breiman and Cutler. We prove the global convergence of the algorithm and show that it can be effectively used for the minimization of extreme eigenvalues, e.g., the largest eigenvalue or the sum of the largest specified number of eigenvalues. This is particularly facilitated by the analytical formulas for the first derivatives of eigenvalues, as well as analytical lower bounds on the second derivatives that can be deduced for extreme eigenvalue functions. The applications that we have in mind also include the H-infinity-norm of a linear dynamical system, numerical radius, distance to uncontrollability, and various other nonconvex eigenvalue optimization problems, for which, generically, the eigenvalue function involved is simple at all points.</subfield>
  </datafield>
  <datafield tag="980" ind1=" " ind2=" ">
    <subfield code="a">publication</subfield>
    <subfield code="b">article</subfield>
  </datafield>
  <datafield tag="540" ind1=" " ind2=" ">
    <subfield code="a">Creative Commons Attribution</subfield>
    <subfield code="u">http://www.opendefinition.org/licenses/cc-by</subfield>
  </datafield>
  <datafield tag="100" ind1=" " ind2=" ">
    <subfield code="a">Mengi, Emre</subfield>
    <subfield code="u">Koc Univ, Dept Math, TR-34450 Istanbul, Turkey</subfield>
  </datafield>
  <datafield tag="856" ind1="4" ind2=" ">
    <subfield code="z">md5:009be5e61d7db8ff646e143c0466db8d</subfield>
    <subfield code="s">178</subfield>
    <subfield code="u">https://aperta.ulakbim.gov.trrecord/66919/files/bib-61b82779-0b34-44ae-be85-ba3c2c100012.txt</subfield>
  </datafield>
  <controlfield tag="005">20210316022811.0</controlfield>
  <datafield tag="260" ind1=" " ind2=" ">
    <subfield code="c">2014-01-01</subfield>
  </datafield>
  <datafield tag="024" ind1=" " ind2=" ">
    <subfield code="a">10.1137/130933472</subfield>
    <subfield code="2">doi</subfield>
  </datafield>
  <datafield tag="542" ind1=" " ind2=" ">
    <subfield code="l">open</subfield>
  </datafield>
  <datafield tag="245" ind1=" " ind2=" ">
    <subfield code="a">NUMERICAL OPTIMIZATION OF EIGENVALUES OF HERMITIAN MATRIX FUNCTIONS</subfield>
  </datafield>
  <datafield tag="909" ind1="C" ind2="4">
    <subfield code="v">35</subfield>
    <subfield code="p">SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS</subfield>
    <subfield code="c">699-724</subfield>
    <subfield code="n">2</subfield>
  </datafield>
  <datafield tag="650" ind1="1" ind2="7">
    <subfield code="a">cc-by</subfield>
    <subfield code="2">opendefinition.org</subfield>
  </datafield>
  <datafield tag="700" ind1=" " ind2=" ">
    <subfield code="a">Yildirim, E. Alper</subfield>
    <subfield code="u">Koc Univ, Dept Ind Engn, TR-34450 Istanbul, Turkey</subfield>
  </datafield>
  <datafield tag="700" ind1=" " ind2=" ">
    <subfield code="a">Kilic, Mustafa</subfield>
    <subfield code="u">Koc Univ, Dept Math, TR-34450 Istanbul, Turkey</subfield>
  </datafield>
  <controlfield tag="001">66919</controlfield>
  <datafield tag="980" ind1=" " ind2=" ">
    <subfield code="a">user-tubitak-destekli-proje-yayinlari</subfield>
  </datafield>
</record>