<?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_max_scale"><info><pubdate>04-Apr-2006</pubdate></info><refnamediv><refname>plq_me_max_scale</refname><refpurpose>Piecewise linear quadratic (plq), Maximum scale for Moreau envelope</refpurpose></refnamediv>
  
   
  
   
  
   
  
   
  
   

  
   <refsynopsisdiv><title>Calling Sequence</title><synopsis>scale = plq_me_max_scale(plqf1, ..., plqfN)</synopsis></refsynopsisdiv>

  
   <refsection><title>Parameters</title>
    
      <variablelist>
      
         <varlistentry>
        
            <term>plqf1 ... plqfN</term>
        
            <listitem>
          
               <para>matrices. PLQ functions for which to compute the maximum scale.
          </para>
        
            </listitem>
      
         </varlistentry>
      
         <varlistentry>
        
            <term>scale</term>
        
            <listitem>
          
               <para>constant. The maximum smoothing parameter that plq_me will accept over all the given functions.
          </para>
        
            </listitem>
      
         </varlistentry>
    
      </variablelist>
  
   </refsection>
  
  
   <refsection><title>Description</title>
      
         <para>
        This function computes the maximum smoothing parameter that may be passed as "lambda" or "mu" into <link linkend="plq_me">plq_me</link> such that a set of nonconvex functions have finite Moreau envelopes.  Otherwise, if the smoothing parameter is too high, g* below will be infinite everywhere because a convex hull cannot be computed. The Moreau envelope formula is
        <!--<programlisting><![CDATA[
    Moreau envelope formula:
    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_max_scale/plq_me_max_scale_1.png"/>
					</imageobject>
				</inlinemediaobject>
			</para>
      
         </para>
    
   </refsection>

  
   <refsection><title>Examples</title><programlisting role="example"><![CDATA[
f1 = [0,-1,0,0;%inf,-2,0,0];
plq_me_max_scale(f1),          # -1/2/(-2) == 0.25
f2 = [1,0,1,0;2,0,-1,2;%inf,-3,0,0];
plq_me_max_scale(f2),          # -1/2/(-3) == 0.167
plq_me_max_scale(f1, f2);      # 0.167
  ]]></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>Bryan Gardiner</literal>, University of British Columbia, BC, Canada
  </para></refsection>

</refentry>