<?xml version="1.0" encoding="ISO-8859-1"?><refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="plq_me"><info><pubdate>04-Apr-2006</pubdate></info><refnamediv><refname>plq_me</refname><refpurpose>Piecewise linear quadratic (plq), Moreau envelope</refpurpose></refnamediv>
  
   
  
   
  
   
  
   
  
   

  
   <refsynopsisdiv><title>Calling Sequence</title><synopsis>plqme = plq_me(plqf,lambda,isConvex)</synopsis></refsynopsisdiv>

  
   <refsection><title>Parameters</title>
	  
      <variablelist>
		  
         <varlistentry>
			  
            <term>plqf</term>
			  
            <listitem>
				  
               <para>matrix. A plq function with dimensions n x 4.
				  </para>
			  
            </listitem>
		  
         </varlistentry>
		  
         <varlistentry>
			  
            <term>lambda</term>
			  
            <listitem>
				  
               <para>constant, positive smoothing parameter.
				  </para>
			  
            </listitem>
		  
         </varlistentry>
		 
		 <varlistentry>
			  
            <term>isConvex</term>
			  
            <listitem>
				  
               <para>%t or %f, weather plqf is convex or non-convex.
				  </para>
			  
            </listitem>
		  
         </varlistentry>
		  
         <varlistentry>
			  
            <term>plqme</term>
			  
            <listitem>
				  
               <para>matrix. A plq function with dimensions n x 4.
				  </para>
			  
            </listitem>
		  
         </varlistentry>
	  
      </variablelist>
  
   </refsection>
 
  
   <refsection><title>Description</title>
     
         <para>
	     Compute the Moreau envelope (ME) transform of a convex plq function, where the input and output is given in the form of a plq matrix. The Moreau Envelope is computed using the formula:<!--<programlisting><![CDATA[
    M[lambda](s) = (1/2lambda)||s||^2 - (1/lambda)g*[lambda](s),
    where g[lambda](x) = (1/2)*||x||^2 + lambda*f(x),
      and * represents the Fenchel Conjugate.
]]></programlisting>-->
		<para>
			<inlinemediaobject>
				<imageobject>
					<imagedata fileref="plq_ImagesOfEquationsByLatex/plq_me/plq_me_1.png"/>
				</imageobject>
			</inlinemediaobject>
		</para>
    
         </para>
 	
   </refsection>

  
   <refsection><title>Examples</title><programlisting role="example"><![CDATA[
lambda=1;
fctn = [%inf,1/2,0,0];
result = plq_me(fctn,lambda);
  ]]></programlisting></refsection>


   <refsection><title>See Also</title><simplelist type="inline">	
    
      <member>
         <link linkend="plq_function">plq_function</link>
      </member>

   </simplelist></refsection>

  
   <refsection><title>Authors</title><para>
	  
      <literal>Mike Trienis</literal>, University of British Columbia, BC, Canada
  </para></refsection>

  
   <refsection><title>Used Functions</title>
     
      <para>
       
         <link linkend="plq_me_max_scale">plq_me_max_scale</link> is called when nonconvexity conditions apply.
     </para>
  
   </refsection>

</refentry>