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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>Minimization or Maximization of an Objective Function</h1></td></tr><tr><td class = "DocHeader4" colspan = "2"/></tr><tr><td class = "DocHeader3" colspan = "2"><table class = "DocThemeIntro" id = "table12"><tr><td class = "Intro1Only"><p class = "header"><p class = "abstract">
<span class = "shortdesc">This section deals with the minimization or maximization of
the objective function. </span>

</p>
<ul><li><a href = "#tso-c-usr-terms-minMaxObjFunc__tso-c-user-ObjFun-MaxOrMinObj" id = "toc_rg" title = "">Minimization or Maximization of an Objective</a></li></ul>
</p></td></tr></table></td></tr></table>




<div class = "body conbody">
<p>The optimization formulation consists of an objective function
and a set of constraints as shown in the first equation of <a class = "xref" href = "tso-c-usr-terms-ovw.htm" title = "To optimize something you need to know what to optimize. Do you want to minimize stresses? Or maximize all eigenvalues?">Mathematical Formulation</a>.</p>

<p>The objective can be minimized or maximized using the <code class = "ph codeph">MIN</code> and
                <code class = "ph codeph">MAX</code> in the <code class = "ph codeph">TARGET</code> parameter of the
                <code class = "ph codeph">OBJECTIVE</code> command, respectively. In these cases, the values for the
            objective function defined by the <code class = "ph codeph">DRESP</code>s are summed up.</p>
<p>For example, if the objective should be minimized (or maximized),</p>
<pre class = "codeblock">
<code class = "ph codeph">
OBJ_FUNC
 ID_NAME = ...
 DRESP   = ...
 DRESP   = ...
 ...
 TARGET  = MIN (or MAX)
END_
</code>
</pre>

<p>where the <code class = "ph codeph">DRESP</code> definitions are referring to the desired responses for the
	objective function using the ID name of the defined responses. The defined responses
	that should be minimized (or maximized) must be valid design responses.</p>


<div class = "section" id = "tso-c-usr-terms-minMaxObjFunc__tso-c-user-ObjFun-MaxOrMinObj"><h2 class = "title sectiontitle">Minimization or Maximization of an Objective</h2>

<p>The following tables describe how design responses are handled in an objective function that is to be minimized or maximized:</p>
<table class = "table" id = "tso-c-usr-terms-minMaxObjFunc__ag562874"><caption/><colgroup><col style = "width:33.33333333333333%"/><col style = "width:33.33333333333333%"/><col style = "width:33.33333333333333%"/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-minMaxObjFunc__ag562874__entry__1"><p>Compliance terms for objective</p></th>
<th class = "entry" id = "tso-c-usr-terms-minMaxObjFunc__ag562874__entry__2"><p>Material volume terms for objective</p></th>
<th class = "entry" id = "tso-c-usr-terms-minMaxObjFunc__ag562874__entry__3"><p>Eigenfrequency terms for objective</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-minMaxObjFunc__ag562874__entry__1"><p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">c</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">k</mi></mrow></msub></mrow></math></span></p></td>
<td class = "entry" headers = "tso-c-usr-terms-minMaxObjFunc__ag562874__entry__2"><p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><mi class = "- topic/foreign ">V</mi><mo class = "- topic/foreign ">−</mo><mi class = "- topic/foreign ">V</mi><mo class = "- topic/foreign ">*</mo><mo class = "- topic/foreign ">)</mo></mrow></math></span></p></td>
<td class = "entry" headers = "tso-c-usr-terms-minMaxObjFunc__ag562874__entry__3">
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">f</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">k</mi></mrow></msub></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">−</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">k</mi></mrow></mfrac><mi class = "- topic/foreign ">ln</mi><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mstyle displaystyle = "true" class = "- topic/foreign "><mrow class = "- topic/foreign "><munderover class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">∑</mo></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">j</mi><mo class = "- topic/foreign ">=</mo><mn class = "- topic/foreign ">1</mn></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">n</mi></mrow></munderover><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">−</mo><mi class = "- topic/foreign ">k</mi><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">f</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">j</mi></mrow></msub></mrow></msup></mrow></mstyle><mo class = "- topic/foreign ">)</mo></mrow></mrow></math></span></p></td>
</tr>
</tbody></table>

<table class = "table" id = "tso-c-usr-terms-minMaxObjFunc__ag580798"><caption/><colgroup><col style = "width:33.33333333333333%"/><col style = "width:33.33333333333333%"/><col style = "width:33.33333333333333%"/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-minMaxObjFunc__ag580798__entry__1"><p> Displacement terms for objective</p></th>
<th class = "entry" id = "tso-c-usr-terms-minMaxObjFunc__ag580798__entry__2"><p>Reaction force terms for objective</p></th>
<th class = "entry" id = "tso-c-usr-terms-minMaxObjFunc__ag580798__entry__3"><p>Internal force terms for objective</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-minMaxObjFunc__ag580798__entry__1">
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">θ</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">1</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">1</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">u</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup></mrow></msqrt></mrow></math></span></p></td>
<td class = "entry" headers = "tso-c-usr-terms-minMaxObjFunc__ag580798__entry__2"><p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">M</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">1</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">1</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">R</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup></mrow></msqrt></mrow></math></span></p></td>
<td class = "entry" headers = "tso-c-usr-terms-minMaxObjFunc__ag580798__entry__3">
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">M</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">x</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">y</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup><mo class = "- topic/foreign ">+</mo><msubsup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">z</mi></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msubsup></mrow></msqrt></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">1</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">1</mn></mrow></msub><mo class = "- topic/foreign ">−</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">F</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mo class = "- topic/foreign ">,</mo><mn class = "- topic/foreign ">2</mn></mrow></msub><mo class = "- topic/foreign ">)</mo></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow></msup></mrow></msqrt></mrow></math></span></p></td>
</tr>
</tbody></table>

<table class = "table" id = "tso-c-usr-terms-minMaxObjFunc__ag580840"><caption/><colgroup><col style = "width:33.33333333333333%"/><col style = "width:33.33333333333333%"/><col style = "width:33.33333333333333%"/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-minMaxObjFunc__ag580840__entry__1"><p>Von Mises stress terms for objective</p></th>
<th class = "entry" id = "tso-c-usr-terms-minMaxObjFunc__ag580840__entry__2"><p>Center of gravity terms for objective</p></th>
<th class = "entry" id = "tso-c-usr-terms-minMaxObjFunc__ag580840__entry__3"><p>Moment of inertia terms for objective</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-minMaxObjFunc__ag580840__entry__1"><p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><mi class = "- topic/foreign ">M</mi><mi class = "- topic/foreign ">a</mi><mi class = "- topic/foreign ">x</mi><mo class = "- topic/foreign ">|</mo><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">v</mi><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">M</mi><mi class = "- topic/foreign ">i</mi><mi class = "- topic/foreign ">s</mi><mi class = "- topic/foreign ">e</mi><mi class = "- topic/foreign ">s</mi></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">)</mo><mi class = "- topic/foreign ">²</mi></mrow></msup></mrow></msub></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">(</mo><mi class = "- topic/foreign ">f</mi><mo class = "- topic/foreign ">(</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ρ</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub><mo class = "- topic/foreign ">)</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">r</mi><mi class = "- topic/foreign ">e</mi><mi class = "- topic/foreign ">f</mi></mrow></msub><mo class = "- topic/foreign ">)</mo><mi class = "- topic/foreign ">²</mi></mrow></mfrac><mo class = "- topic/foreign ">⋅</mo><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">σ</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">r</mi><mi class = "- topic/foreign ">e</mi><mi class = "- topic/foreign ">f</mi></mrow></msub><mo class = "- topic/foreign ">|</mo></mrow></math></span></p><p>(Constant temperature loading is supported.)</p></td>
<td class = "entry" headers = "tso-c-usr-terms-minMaxObjFunc__ag580840__entry__2"><p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi></mrow></msub></mrow></math></span></p></td>
<td class = "entry" headers = "tso-c-usr-terms-minMaxObjFunc__ag580840__entry__3"><p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">I</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">i</mi><mi class = "- topic/foreign ">j</mi></mrow></msub></mrow></math></span></p></td>
</tr>
</tbody></table>
<table class = "table"><caption/><colgroup><col style = "width:50%"/><col style = "width:50%"/><col/></colgroup><thead class = "thead">
<tr class = "row">
<th class = "entry" id = "tso-c-usr-terms-minMaxObjFunc__tso-c-user-ObjFun-MaxOrMinObj__entry__19"><p>Plastic strain terms in objective**</p></th>
<th class = "entry" id = "tso-c-usr-terms-minMaxObjFunc__tso-c-user-ObjFun-MaxOrMinObj__entry__20"><p>Thermal terms in objective**</p></th>
</tr>
</thead><tbody class = "tbody">
<tr class = "row">
<td class = "entry" headers = "tso-c-usr-terms-minMaxObjFunc__tso-c-user-ObjFun-MaxOrMinObj__entry__19"><p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msqrt class = "- topic/foreign "><mrow class = "- topic/foreign "><mfrac class = "- topic/foreign "><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">2</mn></mrow><mrow class = "- topic/foreign "><mn class = "- topic/foreign ">3</mn></mrow></mfrac><mrow class = "- topic/foreign "><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">pl</mi></mrow></msup><mo class = "- topic/foreign ">:</mo><msup class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">ε</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">pl</mi></mrow></msup></mrow></mrow></msqrt></mrow></math></span></p></td>
<td class = "entry" headers = "tso-c-usr-terms-minMaxObjFunc__tso-c-user-ObjFun-MaxOrMinObj__entry__20">
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">c</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">T</mi></mrow></msub></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">T</mi></mrow></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">q</mi></mrow></mrow></math></span></p>
<p><span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">+</mo><mi class = "- topic/foreign ">α</mi><mrow class = "- topic/foreign "><munder class = "- topic/foreign "><mo class = "- topic/foreign ">∑</mo><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e</mi></mrow></munder></mrow><mrow class = "- topic/foreign "><munder class = "- topic/foreign "><mo class = "- topic/foreign ">∑</mo><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">n</mi></mrow></munder></mrow><mrow class = "- topic/foreign "><msub class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">Q</mi></mrow><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">e,n</mi></mrow></msub></mrow><mrow class = "- topic/foreign "><mo class = "- topic/foreign ">-</mo><mi class = "- topic/foreign ">q</mi></mrow></mrow></math></span></p></td>
</tr>
</tbody></table>


<p>In this table the indexes <span class = "ph">i</span> and j indicate a direction of an axis (x, y, or z) of the
   global or a local coordinate system. The compliance, eigenfrequencies, displacements, and forces can be
   based on results from different <span class = "ph">load cases</span>.</p>
<p>The reference values marked with "*" are defined in the <code class = "ph codeph">DRESP</code> parameter of the
   <code class = "ph codeph">OBJ_FUNC</code> command. By default, the reference values are zero. The reference
    values can be set individually for each term in the objective function.</p>
<p>You define the weight factors 
   <span class = "ph inlineequation"><math class = "- topic/foreign "><mrow class = "- topic/foreign "><mi class = "- topic/foreign ">α</mi></mrow></math></span>
   in the <code class = "ph codeph">DRESP</code> parameter of the <code class = "ph codeph">OBJ_FUNC</code> command.
   The weight factors are set individually for each term of the objective function. By default, the
   weight factors are set to 1.</p>
<p>In the example below, the weight factor is set to 1.5 and the reference value is set to 4.0:</p>
<pre class = "codeblock">
<code class = "ph codeph">
OBJ_FUNC
...
DRESP = id_dresp, 1.5, 4.0
...
END_
</code>
</pre>

<p><table class = "Remark" id = "table132"><tr><td class = "Remark"><span class = "run-in.important">Important:
				</span><span class = "notecontent"><ul class = "ul">
<li class = "li">A minimization optimization task can be converted into a maximization
optimization task (or vice versa) by changing the sign of the weighting
factors in the definition of the objective function.</li>
<li class = "li">Design responses marked with <code class = "ph codeph">**</code> are allowed only using 
    <span class = "ph">Abaqus</span>
    sensitivities.</li>
</ul></span></td></tr></table>
</p>
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