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      <title>Optimize 1xN Goal Seek</title>
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      <div class="title_topic5" id="xps10_pagetitle">Optimize 1xN Goal Seek</div>
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      <p class="para_topic"> Optimize 1xN allows you to solve problems using multiple variables to control one objective or target function as the output. An example might be where several size and thickness parameters are variables, with strength or weight being the output objective function. You can then use Optimize 1xN Goal Seek to determine values for the input parameters that fit within your defined constraints in order to maximize the strength, or even minimize the weight. If the desired output is to maximize the strength  <em>and</em> minimize the weight, then a single objective function would need to be constructed as a weighted average of strength and weight.
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      <p class="para_topic"> The Optimize 1xN Goal Seek function displays an input dialog in which you specify the control variables, the constraints, and the cell for the objective function. You can specify up to 10 cells as input variables by using a comma between cell references (e.g., A10,B12,C15). You also use commas to separate multiple values for the upper and lower constraints and the starting points. Leaving the constraint values blank means the variable is unconstrained. For multiple input variables, you can constrain some inputs and not others using a syntax such as &quot;0.0,1.0,,,,2.0&quot;. By default, the goal seek attempts to minimize the objective function.</p>
      <p class="para_topic"> Optimize 1xN requires the following information:</p>
      <p class="para_topic"> The optimization function finds a local minimum to the set of equations, where changing any of the input values would result in an output that is less optimum than the current value. As a result, it is possible to have multiple solution points for a set of input equations, and the final output value is dependent on the initial start points for the variable cells. A good initial guess for the input values will help achieve the best answer and improve the performance of the algorithm.</p>
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               <p class="para_td"> Num. Variables</p>
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               <p class="para_td"> The number of input variables.</p>
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               <p class="para_td"> Variable Cell(s)</p>
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               <p class="para_td"> The input variable cells.</p>
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               <p class="para_td"> Start Point(s)</p>
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               <p class="para_td"> The optional initial guess.</p>
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               <p class="para_td"> Min Bound(s)</p>
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               <p class="para_td"> Lower constraint value for an input variable. The value of the input variable will not be allowed to drop below this value.</p>
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               <p class="para_td"> Max Bound(s)</p>
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               <p class="para_td"> Upper constraint value for an input variable.</p>
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               <p class="para_td"> Target Cell</p>
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               <p class="para_td"> The cell location for result.</p>
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               <p class="para_td"> Tolerance</p>
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               <p class="para_td"> The desired accuracy of convergence.</p>
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               <p class="para_td"> Max Iterations</p>
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               <p class="para_td"> The number of iterations allowed.</p>
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      </table><br><p class="para_topic"> On UNIX platforms, if you select the Trace Function check box, the system prints additional information to the terminal window. On Windows platforms, selecting the Trace Function check box has no effect.</p>
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