<?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>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332024000200195</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v31i2.56792</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Gradients and optimization with constraints in economics and social sciences]]></article-title>
<article-title xml:lang="es"><![CDATA[Gradientes y optimización con restricciones en economía y ciencias sociales]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pernice]]></surname>
<given-names><![CDATA[Sergio A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad del CEMA  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Argentina</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2024</year>
</pub-date>
<volume>31</volume>
<numero>2</numero>
<fpage>195</fpage>
<lpage>229</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332024000200195&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332024000200195&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332024000200195&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Despite their widespread use in advanced analytical and numerical techniques, gradient field methods are often underrepresented in the foundational training of economists and social scientists. As machine learning and sophisticated analytical and numerical approaches gain traction, the importance of gradient methods in optimization processes becomes increasingly apparent. This oversight in academic and practical toolsets is suboptimal. This paper aims to address this gap by introducing gradient field methods both intuitively and rigorously, situating them within the context of problems commonly encountered by economists and social scientists, with a particular focus on equality constrained optimization.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen A pesar de su uso generalizado en técnicas analíticas y numéricas avanzadas, los métodos de campo de gradientes suelen estar subrepresentados en la formación básica de economistas y científicos sociales. A medida que el aprendizaje automático y los enfoques analíticos y numéricos sofisticados ganan terreno, la importancia de los métodos de gradiente en los procesos de optimización se vuelve cada vez más evidente. Esta falta en las herramientas académicas y prácticas es subóptima. Este artículo tiene como objetivo abordar esta brecha introduciendo los métodos de campo de gradientes tanto de manera intuitiva como rigurosa, situándolos en el contexto de problemas comúnmente encontrados por economistas y científicos sociales, con un enfoque particular en la optimización con restricciones de igualdad.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Minimización con restricciones]]></kwd>
<kwd lng="es"><![CDATA[Multiplicadores de Lagrange]]></kwd>
<kwd lng="es"><![CDATA[Algoritmos con campos de gradientes.]]></kwd>
<kwd lng="en"><![CDATA[Minimization with constraints]]></kwd>
<kwd lng="en"><![CDATA[Lagrange multipliers]]></kwd>
<kwd lng="en"><![CDATA[Gradient fields algorithms.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Athey]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Impact of Machine Learning on Economics. The Economics of Artificial Intelligence: An Agenda]]></article-title>
<source><![CDATA[University of Chicago Press]]></source>
<year>2019</year>
<page-range>507-47</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Athey]]></given-names>
</name>
<name>
<surname><![CDATA[G,W]]></surname>
<given-names><![CDATA[Imbens]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Machine Learning Methods That Economists Should Know About]]></article-title>
<source><![CDATA[Annual Review of Economics]]></source>
<year>2019</year>
<volume>11</volume>
<page-range>685-725</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Belloni]]></given-names>
</name>
<name>
<surname><![CDATA[V]]></surname>
<given-names><![CDATA[Chernozhukov]]></given-names>
</name>
<name>
<surname><![CDATA[C]]></surname>
<given-names><![CDATA[Hansen]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[High-dimensional methods and inference on structural and treatment effects]]></article-title>
<source><![CDATA[Journal of Economic Perspectives]]></source>
<year>2014</year>
<volume>28</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>29-50</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D]]></surname>
<given-names><![CDATA[Bertsekas]]></given-names>
</name>
</person-group>
<source><![CDATA[Nonlinear Programming]]></source>
<year>2016</year>
<publisher-name><![CDATA[Athena Scientific]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[C]]></surname>
<given-names><![CDATA[Bishop]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Pattern Recognition and Machine Learning]]></article-title>
<source><![CDATA[Information Science and Statistics]]></source>
<year>2016</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Bonnans]]></given-names>
</name>
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Gilbert]]></given-names>
</name>
<name>
<surname><![CDATA[C]]></surname>
<given-names><![CDATA[Lemarechal]]></given-names>
</name>
<name>
<surname><![CDATA[C]]></surname>
<given-names><![CDATA[Sagastizábal]]></given-names>
</name>
</person-group>
<source><![CDATA[Numerical Optimization: Theoretical and Practical Aspects]]></source>
<year>2013</year>
<publisher-loc><![CDATA[Berlin Heidelberg ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Boyd]]></given-names>
</name>
<name>
<surname><![CDATA[L]]></surname>
<given-names><![CDATA[Vandenberghe]]></given-names>
</name>
</person-group>
<source><![CDATA[Convex Optimization]]></source>
<year>2004</year>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[V]]></surname>
<given-names><![CDATA[Chernozhukov]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Double/debiased machine learning for treatment and structural parameters]]></article-title>
<source><![CDATA[The Econometrics Journal]]></source>
<year>2018</year>
<volume>21</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>C1-C68</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Chiang]]></given-names>
</name>
<name>
<surname><![CDATA[K]]></surname>
<given-names><![CDATA[Wainwright]]></given-names>
</name>
</person-group>
<source><![CDATA[Fundamental Methods of Mathematical Economics]]></source>
<year>2005</year>
<edition>McGraw-Hill international edition</edition>
<publisher-name><![CDATA[McGraw-Hill Education]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Duchi]]></given-names>
</name>
<name>
<surname><![CDATA[E]]></surname>
<given-names><![CDATA[Hazan]]></given-names>
</name>
<name>
<surname><![CDATA[Y]]></surname>
<given-names><![CDATA[Singer]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Adaptive Subgradient Methods for Online Learning and Stochastic Optimization]]></article-title>
<source><![CDATA[Journal of Machine Learning Research]]></source>
<year>2011</year>
<volume>12</volume>
<numero>61</numero>
<issue>61</issue>
<page-range>2121-59</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[I]]></surname>
<given-names><![CDATA[Goodfellow]]></given-names>
</name>
<name>
<surname><![CDATA[Y]]></surname>
<given-names><![CDATA[Bengio]]></given-names>
</name>
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Courville]]></given-names>
</name>
</person-group>
<source><![CDATA[Deep Learning. Adaptive Computation and Machine Learning series]]></source>
<year>2016</year>
<publisher-name><![CDATA[MIT Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Grimmer]]></given-names>
</name>
<name>
<surname><![CDATA[M,E]]></surname>
<given-names><![CDATA[Roberts]]></given-names>
</name>
<name>
<surname><![CDATA[B,M]]></surname>
<given-names><![CDATA[Stewart]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Machine learning for social science: An agnostic approach]]></article-title>
<source><![CDATA[Annual Review of Political Science]]></source>
<year>2021</year>
<volume>24</volume>
<page-range>395-419</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[M]]></surname>
<given-names><![CDATA[Hoy]]></given-names>
</name>
<name>
<surname><![CDATA[Press]]></surname>
<given-names><![CDATA[The MIT]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematics for Economics]]></source>
<year>2011</year>
<edition>third edition</edition>
<publisher-name><![CDATA[MIT Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[W]]></surname>
<given-names><![CDATA[Karush]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Minima of Functions of Several Variables with Inequalities as Side Conditions]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[G]]></surname>
<given-names><![CDATA[Giorgi]]></given-names>
</name>
<name>
<surname><![CDATA[T,H]]></surname>
<given-names><![CDATA[Kjeldsen]]></given-names>
</name>
</person-group>
<source><![CDATA[Traces and Emergence of Nonlinear Programming]]></source>
<year>2014</year>
<page-range>217-45</page-range><publisher-loc><![CDATA[Basel ]]></publisher-loc>
<publisher-name><![CDATA[Springer Basel]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D,P]]></surname>
<given-names><![CDATA[Kingma]]></given-names>
</name>
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Ba]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Adam: A method for stochastic optimization]]></article-title>
<source><![CDATA[arXiv preprint]]></source>
<year>2014</year>
</nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Kleinberg]]></given-names>
</name>
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Ludwig]]></given-names>
</name>
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Mullainathan]]></given-names>
</name>
<name>
<surname><![CDATA[C,R]]></surname>
<given-names><![CDATA[Sunstein]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Discrimination in the Age of Algorithms]]></article-title>
<source><![CDATA[Journal of Legal Analysis]]></source>
<year>2019</year>
<volume>10</volume>
<page-range>113-74</page-range></nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[H]]></surname>
<given-names><![CDATA[Kuhn]]></given-names>
</name>
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Tucker]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Nonlinear Programming]]></article-title>
<source><![CDATA[Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability]]></source>
<year>1951</year>
</nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[R,P]]></surname>
<given-names><![CDATA[Masini]]></given-names>
</name>
<name>
<surname><![CDATA[M,C]]></surname>
<given-names><![CDATA[Medeiros]]></given-names>
</name>
<name>
<surname><![CDATA[E,F]]></surname>
<given-names><![CDATA[Mendes]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Machine learning advances for time series forecasting]]></article-title>
<source><![CDATA[Journal of economic surveys]]></source>
<year>2023</year>
<volume>37</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>76-111</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Mullainathan]]></given-names>
</name>
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Spiess]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Machine learning: &lt;an applied econometric approach]]></article-title>
<source><![CDATA[Journal of Economic Perspectives]]></source>
<year>2017</year>
<volume>31</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>87-106</page-range></nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Nocedal]]></given-names>
</name>
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Wright]]></given-names>
</name>
</person-group>
<source><![CDATA[Numerical Optimization]]></source>
<year>2006</year>
<publisher-name><![CDATA[Springer New York]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Noy]]></given-names>
</name>
<name>
<surname><![CDATA[W]]></surname>
<given-names><![CDATA[Zhang]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Experimental evidence on the productivity effects of generative artificial intelligence]]></article-title>
<source><![CDATA[Science]]></source>
<year>2023</year>
<volume>381</volume>
<numero>6654</numero>
<issue>6654</issue>
<page-range>187-92</page-range></nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D]]></surname>
<given-names><![CDATA[Rolnick]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Tackling climate change with machine learning]]></article-title>
<source><![CDATA[ACM Computing Surveys (CSUR)]]></source>
<year>2022</year>
<volume>55</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>1-96</page-range></nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[S]]></surname>
<given-names><![CDATA[Ruder]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An overview of gradient descent optimization algorithms]]></article-title>
<source><![CDATA[arXiv preprint]]></source>
<year>2016</year>
</nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[C]]></surname>
<given-names><![CDATA[Simon]]></given-names>
</name>
<name>
<surname><![CDATA[L]]></surname>
<given-names><![CDATA[Blume]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematics for Economists]]></source>
<year>1994</year>
<publisher-loc><![CDATA[Norton ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[H,R]]></surname>
<given-names><![CDATA[Varian]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Big data: New tricks for econometrics]]></article-title>
<source><![CDATA[Journal of Economic Perspectives]]></source>
<year>2014</year>
<volume>28</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>3-28</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
