<?xml version="1.0" encoding="iso-8859-1"?>
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  <info>
    <pubdate>17-May-2010</pubdate>
  </info>

  <refnamediv>
    <refname>opt_lft</refname>
    <refpurpose>Convex operators via optimization (OPT), Legendre-Fenchel transform (LFT)</refpurpose>
  </refnamediv>

   <refsynopsisdiv>
     <title>Calling Sequence</title>
     <synopsis>[y, argmin] = opt_lft(f, df, domf, s, output)</synopsis>
   </refsynopsisdiv>

   <refsection>
     <title>Parameters</title>
     <variablelist>

       <varlistentry>
         <term>f</term>
         <listitem>
           <para>Univariate function, continuous but (potentially) nonsmooth.</para>
         </listitem>
       </varlistentry>

       <varlistentry>
         <term>df</term>
         <listitem>
           <para>Univariate function: derivative of f.</para>
         </listitem>
       </varlistentry>

       <varlistentry>
         <term>domf</term>
         <listitem>
           <para>Domain of the function f (set of points where the
           function is finite).  Domains are stored as intervals
           I=[lb,ub] with ub&lt;lb storing an empty set.</para>
         </listitem>
       </varlistentry>

       <varlistentry>
         <term>s</term>
         <listitem>
           <para>Vector of points at which to evaluate the LFT.</para>
         </listitem>
       </varlistentry>

       <varlistentry>
         <term>output</term>
         <listitem>
           <para>0: no output, 1: progress bar.</para>
         </listitem>
       </varlistentry>

       <varlistentry>
         <term>y</term>
         <listitem>
           <para>The values of the LFT evaluated at each x.</para>
         </listitem>
       </varlistentry>

       <varlistentry>
         <term>argmin</term>
         <listitem>
           <para>A point at which the LFT attains its minimum, for
           each x.</para>
         </listitem>
       </varlistentry>

     </variablelist>
   </refsection>

   <refsection>
     <title>Description</title>

     <para>
       Computes the Legendre-Fenchel transform of f evaluated on
       vector s, giving the values y such that

       <!--<programlisting><![CDATA[
    y = f^*(s) = sup [s*x - f(x)] .
                  x
]]></programlisting>-->
		<para>
			<inlinemediaobject>
				<imageobject>
					<imagedata fileref="opt_ImagesOfEquationsByLatex/opt_lft/opt_lft_1.png"/>
				</imageobject>
			</inlinemediaobject>
		</para>
     </para>
   </refsection>

   <refsection>
     <title>Authors</title>
     <para>
       <simplelist>
         <member>
           Yves Lucet, University of British Columbia, BC, Canada
         </member>
       </simplelist>
     </para>
   </refsection>

</refentry>
