<?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>1405-5546</journal-id>
<journal-title><![CDATA[Computación y Sistemas]]></journal-title>
<abbrev-journal-title><![CDATA[Comp. y Sist.]]></abbrev-journal-title>
<issn>1405-5546</issn>
<publisher>
<publisher-name><![CDATA[Instituto Politécnico Nacional, Centro de Investigación en Computación]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1405-55462018000200315</article-id>
<article-id pub-id-type="doi">10.13053/cys-22-2-2943</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Solvability and Primal-dual Partitions of the Space of Continuous Linear Semi-infinite Optimization Problems]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Barragán]]></surname>
<given-names><![CDATA[Abraham]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Hernández]]></surname>
<given-names><![CDATA[Lidia]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Todorov]]></surname>
<given-names><![CDATA[Maxim]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,BUAP  ]]></institution>
<addr-line><![CDATA[Puebla ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,UDLAP  ]]></institution>
<addr-line><![CDATA[Puebla ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<volume>22</volume>
<numero>2</numero>
<fpage>315</fpage>
<lpage>329</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1405-55462018000200315&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1405-55462018000200315&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1405-55462018000200315&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: Different partitions of the parameter space of all linear semi-infinite programming problems with a fixed compact set of indices and continuous right and left hand side coefficients have been considered in this paper. The optimization problems are classified in a different manner, e.g., consistent and inconsistent, solvable (with bounded optimal value and nonempty optimal set), unsolvable (with bounded optimal value and empty optimal set) and unbounded (with infinite optimal value). The classification we propose generates a partition of the parameter space, called second general primal-dual partition. We characterize each cell of the partition by means of necessary and sufficient, and in some cases only necessary or sufficient conditions, assuring that the pair of problems (primal and dual), belongs to that cell. In addition, we show non emptiness of each cell of the partition and with plenty of examples we demonstrate that some of the conditions are only necessary or sufficient. Finally, we investigate various questions of stability of the presented partition.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Linear semi-infinite programming]]></kwd>
<kwd lng="en"><![CDATA[parameter space of continuous problems]]></kwd>
<kwd lng="en"><![CDATA[primal-dual partition]]></kwd>
<kwd lng="en"><![CDATA[stability properties]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Amaya]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Gómez]]></surname>
<given-names><![CDATA[J. A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Strong duality for inexact linear programming problems]]></article-title>
<source><![CDATA[Optimization]]></source>
<year>2001</year>
<volume>49</volume>
<page-range>243-69</page-range></nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Barragán]]></surname>
<given-names><![CDATA[A. B.]]></given-names>
</name>
<name>
<surname><![CDATA[Hernández]]></surname>
<given-names><![CDATA[L. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Todorov]]></surname>
<given-names><![CDATA[M. I.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[New primal-dual partition of the space of linear semi-infinite continuous optimization problems]]></article-title>
<source><![CDATA[Comptes rendus]]></source>
<year>2016</year>
<volume>69</volume>
<page-range>1263-74</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Betro]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Guglielmi]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Methods for global prior robustness under generalized moment conditions]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Ríos]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Ruggeri]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<source><![CDATA[Robust Bayesian Analysis]]></source>
<year>2000</year>
<page-range>273-93</page-range><publisher-loc><![CDATA[N.Y ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dahl]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Claesson]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Nordebo]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Nordholm]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Chebyshev optimization of circular arrays]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Yang]]></surname>
<given-names><![CDATA[X.]]></given-names>
</name>
</person-group>
<source><![CDATA[Optimization Methods and Applications]]></source>
<year>2001</year>
<page-range>309-19</page-range><publisher-loc><![CDATA[Dordrecht ]]></publisher-loc>
<publisher-name><![CDATA[Kluwer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dolgin]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Zeheb]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Model reduction of uncertain FIR discrete-time systems]]></article-title>
<source><![CDATA[IEEE Trans. Circuits and Systems]]></source>
<year>2004</year>
<volume>51</volume>
<page-range>406-11</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dolgin]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Zeheb]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Model reduction of uncertain systems retaining the uncertainty structure]]></article-title>
<source><![CDATA[Systems and Control Letters]]></source>
<year>2005</year>
<volume>54</volume>
<page-range>771-9</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Duer]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Jargalsaikhan]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Still]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Genericity results in linear conic programming - a tour d&#8217;horizon]]></article-title>
<source><![CDATA[Mathematics of Operations Research]]></source>
<year>2018</year>
</nlm-citation>
</ref>
<ref id="B8">
<label>8</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Goberna]]></surname>
<given-names><![CDATA[M. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Jornet]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Puente]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Optimización Lineal. Teoría, Métodos y Modelos]]></source>
<year>2004</year>
<publisher-loc><![CDATA[Madrid ]]></publisher-loc>
<publisher-name><![CDATA[Mc Graw Hill]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<label>9</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Goberna]]></surname>
<given-names><![CDATA[M. A.]]></given-names>
</name>
<name>
<surname><![CDATA[López]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Linear Semi-infinite Optimization]]></source>
<year>1998</year>
<publisher-loc><![CDATA[Chichester ]]></publisher-loc>
<publisher-name><![CDATA[Wiley]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<label>10</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Goberna]]></surname>
<given-names><![CDATA[M. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Todorov]]></surname>
<given-names><![CDATA[M. I.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Generic Primal-dual solvability in continuous linear semi-infinite optimization]]></article-title>
<source><![CDATA[Optimization]]></source>
<year>2008</year>
<volume>57</volume>
<page-range>239-48</page-range></nlm-citation>
</ref>
<ref id="B11">
<label>11</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Goberna]]></surname>
<given-names><![CDATA[M. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Todorov]]></surname>
<given-names><![CDATA[M. I.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Primal-dual stability in continuous linear optimization]]></article-title>
<source><![CDATA[Mathematical Programming]]></source>
<year>2009</year>
<volume>116B</volume>
<page-range>129-47</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>12</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kortanek]]></surname>
<given-names><![CDATA[K. O.]]></given-names>
</name>
<name>
<surname><![CDATA[Medvedev]]></surname>
<given-names><![CDATA[V. G.]]></given-names>
</name>
</person-group>
<source><![CDATA[Building and Using Dynamic Interest Rate Models, J.]]></source>
<year>2001</year>
<publisher-loc><![CDATA[Chichester ]]></publisher-loc>
<publisher-name><![CDATA[Wiley]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<label>13</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nordholm]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Nordberg]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Claesson]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Nordebo]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Beamforming and interference cancellation for capacity gain in mobile networks]]></article-title>
<source><![CDATA[Ann. Oper. Res]]></source>
<year>2001</year>
<volume>98</volume>
<page-range>235-53</page-range></nlm-citation>
</ref>
<ref id="B14">
<label>14</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Noubiap]]></surname>
<given-names><![CDATA[R. F.]]></given-names>
</name>
<name>
<surname><![CDATA[Seidel]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An algorithm for calculating Gamma-minimax decision rules under generalized moment conditions]]></article-title>
<source><![CDATA[Ann. Stat]]></source>
<year>2001</year>
<volume>29</volume>
<page-range>1094-116</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>15</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ochoa]]></surname>
<given-names><![CDATA[P. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Vera de Serio]]></surname>
<given-names><![CDATA[V. N.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Stability of the primal-dual partition in linear semi-infinite programming]]></article-title>
<source><![CDATA[Optimization]]></source>
<year>2012</year>
<volume>61</volume>
<page-range>1449-65</page-range></nlm-citation>
</ref>
<ref id="B16">
<label>16</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sabharwal]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Avidor]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Potter]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Sector beam synthesis for cellular systems using phased antenna arrays]]></article-title>
<source><![CDATA[IEEE Trans. on Vehicular Tech]]></source>
<year>2000</year>
<volume>49</volume>
<page-range>1784-92</page-range></nlm-citation>
</ref>
<ref id="B17">
<label>17</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Todorov]]></surname>
<given-names><![CDATA[M. I]]></given-names>
</name>
</person-group>
<source><![CDATA[Linear Inequality Systems: Qualitative Stability and New Concepts of Active Constraints]]></source>
<year>2010</year>
<volume>54</volume>
<publisher-name><![CDATA[Hozlo, S.R.L.]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
