<?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>0120-419X</journal-id>
<journal-title><![CDATA[Revista Integración]]></journal-title>
<abbrev-journal-title><![CDATA[Integración - UIS]]></abbrev-journal-title>
<issn>0120-419X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Industrial de Santander]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-419X2021000200191</article-id>
<article-id pub-id-type="doi">10.18273/revint.v39n2-20210004</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[A global Jacobian smoothing algorithm for nonlinear complementarity problems]]></article-title>
<article-title xml:lang="es"><![CDATA[Un algoritmo global con jacobiano suavizado para problemas de complementariedad no lineal]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[SÁNCHEZ]]></surname>
<given-names><![CDATA[WILMER]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[PÉREZ]]></surname>
<given-names><![CDATA[ROSANA]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[MARTÍNEZ]]></surname>
<given-names><![CDATA[HÉCTOR J.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad del Cauca Departamento de Matemáticas ]]></institution>
<addr-line><![CDATA[Popayán ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad del Cauca Departamento de Matemáticas ]]></institution>
<addr-line><![CDATA[Popayán ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad del Valle Departamento de Matemáticas ]]></institution>
<addr-line><![CDATA[Cali ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<volume>39</volume>
<numero>2</numero>
<fpage>191</fpage>
<lpage>215</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2021000200191&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2021000200191&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2021000200191&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract. In this paper, we use the smoothing Jacobian strategy to propose a new algorithm for solving complementarity problems based on its reformulation as a nonsmooth system of equations. This algorithm can be seen as a generalization of the one proposed in [18]. We develop its global convergence theory and under certain assumptions, we demonstrate that the proposed algorithm converges locally and, q-superlinearly or q-quadratically to a solution of the problem. Some numerical experiments show a good performance of this algorithm. MSC2010: 49M15, 90C06, 90C30.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen. En este artículo, usamos la estrategia del jacobiano suavizado para proponer un nuevo algoritmo para resolver problemas de complementariedad no lineal basado en su reformulación como un sistema de ecuaciones no lineales. Este algoritmo puede verse como una generalización del propuesto en [18]. Desarrollamos su teoría de convergencia global y bajo ciertas hipótesis, demostramos que el algoritmo converge local y q superlineal o q cuadráticamente a la solución del problema. Pruebas numéricas muestran un buen desempeño del algoritmo propuesto.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Nonlinear complementarity problems]]></kwd>
<kwd lng="en"><![CDATA[complementarity function]]></kwd>
<kwd lng="en"><![CDATA[generalized Newton methods]]></kwd>
<kwd lng="en"><![CDATA[Jacobian smoothing method]]></kwd>
<kwd lng="en"><![CDATA[global convergence]]></kwd>
<kwd lng="en"><![CDATA[superlinear convergence]]></kwd>
<kwd lng="en"><![CDATA[quadratic convergence]]></kwd>
<kwd lng="es"><![CDATA[Complementariedad no lineal]]></kwd>
<kwd lng="es"><![CDATA[función de complementariedad]]></kwd>
<kwd lng="es"><![CDATA[método de Newton generalizado]]></kwd>
<kwd lng="es"><![CDATA[Jacobiano suavizado]]></kwd>
<kwd lng="es"><![CDATA[convergencia global]]></kwd>
<kwd lng="es"><![CDATA[convergencia superlineal]]></kwd>
<kwd lng="es"><![CDATA[convergencia cuadrática]]></kwd>
</kwd-group>
</article-meta>
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