<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0874-5161</journal-id>
<journal-title><![CDATA[Investigação Operacional]]></journal-title>
<abbrev-journal-title><![CDATA[Inv. Op.]]></abbrev-journal-title>
<issn>0874-5161</issn>
<publisher>
<publisher-name><![CDATA[APDIO - Associação Portuguesa de Investigação Operacional]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0874-51612005000200006</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[An extension of a variant of a predictor-corrector primal-dual method from linear programming to semidefinite programming]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Bastos]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Teixeira]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<xref ref-type="aff" rid="A02"/>
<xref ref-type="aff" rid="A03"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidade de Lisboa Departamento de Estatística e Investigação Operacional ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
</aff>
<aff id="A02">
<institution><![CDATA[,Universidade de Trás-os-Montes e Alto Douro, Vila Real Departamento de Matemática ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
</aff>
<aff id="A03">
<institution><![CDATA[,CIO - Centro de Investigação Operacional  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2005</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2005</year>
</pub-date>
<volume>25</volume>
<numero>2</numero>
<fpage>253</fpage>
<lpage>276</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://scielo.pt/scielo.php?script=sci_arttext&amp;pid=S0874-51612005000200006&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://scielo.pt/scielo.php?script=sci_abstract&amp;pid=S0874-51612005000200006&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://scielo.pt/scielo.php?script=sci_pdf&amp;pid=S0874-51612005000200006&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[We extend a variant of a predictor-corrector primal-dual method for Linear Programming to Semidefinite Programming. Two versions are proposed. One of the versions uses the HKM direction and the other the NT direction. We present the algorithms associated with these versions and the computational experience using the SDPLIB 1.2 collection of Semidefinite Programming test problems. We show that, in general, the algorithm using the HKM direction is the best and is also better than the one relative to the classical method.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Semidefinite Programming]]></kwd>
<kwd lng="en"><![CDATA[predictor-corrector interior point variant]]></kwd>
<kwd lng="en"><![CDATA[HKM direction]]></kwd>
<kwd lng="en"><![CDATA[NT direction]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ <p align="center"><b>An extension of a variant of a predictor-corrector primal-dual    method from linear programming to semidefinite programming</b></p>      <p align="center">F. Bastos * &#8225;</p>         <p align="center">A. Teixeira * &#8224;</p>     <p align="center">&#8225Departamento de Estatística e Investigação Operacional,    Universidade de Lisboa</p>     <p align="center"><a href="mailto:fbastos@fc.ul.pt">fbastos@fc.ul.pt</a></p>     <p align="center">&#8224 Departamento de Matiática, Universidade de Trás-os-Montes    e Alto Douro, Vila Real</p>     <p align="center"><a href="mailto:ateixeir@utad.pt">ateixeir@utad.pt</a></p>     <p align="center">* CIO - Centro de Investigação Operacional</p>     <p align="center">&nbsp;</p>     <p align="center"></p>     ]]></body>
<body><![CDATA[<p align="center"><b >Abstract</b></p>         <p align="justify" >We extend a variant of a predictor-corrector primal-dual method    for Linear Programming to Siidefinite Programming. Two versions are proposed.    One of the versions uses the HKM direction and the other the NT direction. We    present the algorithms associated with these versions and the computational    experience using the SDPLIB 1.2 collection of Semidefinite Programming test    problis. We show that, in general, the algorithm using the HKM direction is    the best and is also better than the one relative to the classical method.</p>      <p><b>Keywords:</b> Semidefinite Programming, predictor-corrector interior point    variant, HKM direction, NT direction. </p>      <p>&nbsp;</p>      <p>Texto completo apenas disponível em PDF. </p>     <p>Full text only in PDF. </p>        <p>&nbsp;</p>     <p><b>References&nbsp;</b></p>        <!-- ref --><p align="justify">F. Alizadeh, <i>Interior point methods in semidefinite programming    with applications to combinatorial optimization</i>, SIAM Journal Optimization,    5(1) (1995), 13-51.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=328753&pid=S0874-5161200500020000600001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><p align="justify">F. J. Bastos, <i>Problemas de transporte e métodos de ponto    interior</i>, Dissertação de Doutoramento, Universidade Nova de Lisboa, Lisboa,    1994.</p>     ]]></body>
<body><![CDATA[<p align="justify">R. Bellman, K. Fan, <i>On systems of linear inequalities in    Hermitian matrix variables</i>, V. L. Klee (editor), Convexity, Proceedings    of Symposia in Pure Mathematics, American Mathematical Society, 7 (1963), 1-11.</p>     <p align="justify">B. Borchers, CSDP, <i>a C library for semidefinite programming</i>,    Optimization Methods and Software, 11(1) (1999), 613-623.</p>     <p align="justify">B. Borchers, <i>SDPLIB 1.2, a library for semidefinite programming    test problems,</i> Optimization Methods and Software, 11(1) (1999), 683-690.</p>     <p align="justify">B. Borchers, <i>CSDP 3.2, User's Guide</i>, Technical Report,    Department of Mathematics, <st1:State><st1:place>New Mexico</st1:place></st1:State>    <st1:place><st1:City>Tech</st1:City>, <st1:country-region>USA</st1:country-region></st1:place>,    2000.</p>     <p align="justify">B. Borchers, <i>Implementation issues in CSDP</i>, Technical    Report, Department of Mathematics, New Mexico Tech, <st1:country-region><st1:place>USA</st1:place></st1:country-region>,    2001.</p>     <p align="justify">C. Helmberg, F. Rendl, R. J. Vanderbei, H. Wolkowicz, <i>An    interior-point method for semidefinite programming</i>, SIAM Journal Optimization,    6(2) (1996), 342-361.</p>     <p align="justify">R. Horn, C. Johnson, <i>Matrix Analysis</i> , <st1:place><st1:PlaceName>Cambridge</st1:PlaceName>    <st1:PlaceType>University</st1:PlaceType></st1:place> Press, <st1:City><st1:place>Cambridge</st1:place></st1:City>,    1991.</p>     <p align="justify">R. Horn, C. Johnson, <i>Topics in Matrix Analysis</i>, <st1:place><st1:PlaceName>Cambridge</st1:PlaceName>    <st1:PlaceType>University</st1:PlaceType></st1:place> Press, <st1:City><st1:place>Cambridge</st1:place></st1:City>,    1991.</p>     <p align="justify">M. Kojima, <st1:place>S. Shindoh</st1:place>, S. Hara, <i>Interior-point    methods for the monotone semidefinite linear complementary problem in symmetric    matrices</i>, SIAM Journal Optimization, 7(1) (1997), 86-125.</p>     <p align="justify">L. Lovász, <i>On the <st1:place>Shannon</st1:place> Capacity    of a Graph</i>, IEEE Transactions of Information Theory, IT-25(1) (1979), 1-7.</p>     ]]></body>
<body><![CDATA[<p align="justify" >R. D. C. Monteiro, <i>Primal-dual path-following algorithms    for semidefinite programming</i>, SIAM Journal Optimization, 7(3)(1997), 663-678.</p>     <p align="justify">A. Nemirovskii, Y. Nesterov, Interior-Point Polynomial Algorithms    in Convex Programming, Society for Industrial and Applied Mathematics, <st1:City><st1:place>Philadelphia</st1:place></st1:City>,    1994.</p>     <p align="justify">Y. E. Nesterov, M. J. Todd, <i>Self-scaled barriers and interior-point    methods for convex programming</i>, Mathematics of Operations Research, 22(1)    (1997), 1-42.</p>     <p align="justify">M. J. Todd, <i>A study of search directions in primal-dual    interior-point methods for semidefinite programming</i>, Optimization Methods    and Software, 11 (1999), 1-46.</p>     <p align="justify">M. J. Todd, K. C. Toh, R. H. Tutuncu, <i>On the Nesterov-Todd    direction in semidefinite programming</i>, SIAM Journal Optimization, 8(3) (1998),    769-796. </p>     <p align="justify">&nbsp;</p>       <p>&nbsp;</p>         ]]></body><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Alizadeh]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[Interior point methods in semidefinite programming with applications to combinatorial optimization]]></article-title>
<source><![CDATA[SIAM Journal Optimization]]></source>
<year>1995</year>
<volume>1</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>13-51</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
