<?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_pa"><info><pubdate>04-Apr-2006</pubdate></info><refnamediv><refname>plq_pa</refname><refpurpose>Piecewise linear quadratic (plq), convex proximal average via conjugates</refpurpose></refnamediv>
  
   
  
   
  
   
  
   
  
   

  
   <refsynopsisdiv><title>Calling Sequence</title><synopsis>pa = plq_pa(f1,f2,lambda_pa)</synopsis></refsynopsisdiv>

  
   <refsection><title>Parameters</title>
	  
      <variablelist>
		  
         <varlistentry>
			  
            <term>f1</term>
			  
            <listitem>
				  
               <para>matrix. A plq function with dimensions n x 4.
				  </para>
			  
            </listitem>
		  
         </varlistentry>
		  
         <varlistentry>
			  
            <term>f2</term>
			  
            <listitem>
				  
               <para>matrix. A plq function with dimensions n x 4.
				  </para>
			  
            </listitem>
		  
         </varlistentry>
		  
         <varlistentry>
			  
            <term>lambda_pa</term>
			  
            <listitem>
				  
               <para>constant. An intermediate function.
				  </para>
			  
            </listitem>
		  
         </varlistentry>
		  
         <varlistentry>
			  
            <term>pa</term>
			  
            <listitem>
				  
               <para>matrix. A plq function with dimensions n x 4.
				  </para>
			  
            </listitem>
		  
         </varlistentry>
	  
      </variablelist>
  
   </refsection>
 
  
   <refsection><title>Description</title>
     
         <para>
	     Compute the proximal average (PA) of two plq functions at a specified lambda_pa value. The PA is computed using the following formula, where * represents the Fenchel Conjugate.
<!--<programlisting><![CDATA[
    P(f1,lambda,f2) = [ (1 - lambda)(f1 + (1/2)||.||^2)* + lambda(f2 + (1/2)||.||^2)* ]* - (1/2)||.||^2
]]></programlisting>-->
			<para>
				<inlinemediaobject>
					<imageobject>
						<imagedata fileref="plq_ImagesOfEquationsByLatex/plq_pa/plq_pa_1.png"/>
					</imageobject>
				</inlinemediaobject>
			</para>
    
         </para>
 	
   </refsection>

  
   <refsection><title>Examples</title><programlisting role="example"><![CDATA[
lambda_pa = 0.5;
f1 = [%inf, 0, 1, 0];
f2 = [%inf, 0, -1, 5]; 
result = plq_pa(f1, f2, lambda_pa);
  ]]></programlisting></refsection>


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

   </simplelist></refsection>

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

</refentry>