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<a name = "hj-top"> </a><table class = "table1" id = "table11"><tr><td><table class = "DocHeader"><tr><td class = "DocHeader1" colspan = "2"><h1>Update Strategy of the Convex Separable Approximations</h1></td></tr><tr><td class = "DocHeader4" colspan = "2"/></tr><tr><td class = "DocHeader3"><table class = "DocHeaderIntro" id = "table12"><tr><td class = "Intro1Only"><p class = "shortdesc">The relative material volumes of elements of the structure are updated
using the method of Convex Separable Approximations (CSA), see Svanberg (2002). 
</p></td></tr></table></td><td class = "DocHeader2"><table class = "DocTopicsSeeAlso" id = "table13"><tr><td class = "TopicsTitle">See Also</td></tr></table><table class = "DocTopicsInOtherGuides" id = "table14"><tr><td height = "8px"/></tr><tr><td class = "TopicsTitleNormal">In Other Guides</td></tr><tr><td><a title = "Defines parameters to control optimization." href = "../TsoCmdMap/tso-r-cmd-optParam.htm#tso-r-cmd-optParam">OPT_PARAM</a></td></tr></table></td></tr></table>




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<p>Normally,
the update method suggested in Svanberg (2002) is stable. However, if
the design responses are very sensitive, it is suggested to use a more
conservative update method that requires more optimization iterations.
The update strategy is changed using the parameter <code class = "ph codeph">DENSITY_UPDATE</code>.
The default value of <code class = "ph codeph">DENSITY_UPDATE is NORMAL</code>. Setting
<code class = "ph codeph">DENSITY_UPDATE</code> to <code class = "ph codeph">CONSERVATIVE</code> leads
to a conservative update of the design variables:</p>
<pre class = "codeblock">
<code class = "ph codeph">
OPT_PARAM
 ID_NAME        = opt_params
 OPTIMIZE       = id_of_optimize
 DENSITY_UPDATE = CONSERVATIVE
END_
</code>
</pre>
<p><div class = "note collapse"><span class = "run-in.note">Note:
    		</span><span class = "notecontent">The conservative update method is recommended if it is problematic to fulfill the
    constraints used in the optimization formulation.</span></div>
</p>
<p>In addition, you can use a more aggressive update of the design variables to reduce the number of
   optimization iterations by setting <code class = "ph codeph">DENSITY_UPDATE to AGGRESSIVE</code>:</p>
<pre class = "codeblock">
<code class = "ph codeph">
OPT_PARAM
 ID_NAME        = opt_params
 OPTIMIZE       = id_of_optimize
 DENSITY_UPDATE = AGGRESSIVE
END_
</code>
</pre>
<p><table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.warning">Warning:
				</span><span class = "notecontent">This might lead to unstable optimization or prevent the convergence.</span></td></tr></table>
</p>
</div>

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