title: OpenMDAO 1.2.0 implicit component
body: <p>I new to OpenMDAO and I'm still learning how to formulate the problems.
  For a simple example, let's say I have 3 input variables with the given bounds:</p>
  
  <pre><code>1 &lt;= x &lt;= 10
  0 &lt;= y &lt;= 10
  1 &lt;= z &lt;= 10
  </code></pre>
  
  <p>and I have 4 outputs, defined as:</p>
  
  <pre><code>f1 = x * y
  f2 = 2 * z
  g1 = x + y - 1
  g2 = z
  </code></pre>
  
  <p>my goal is to minimize f1 * g1, but enforce the constraint f1 = f2 and g1 = g2.  For example, one solution is x=3, y=4, z=6 (no idea if this is optimal).</p>
  
  <p>For this simple problem, you can probably just feed the output equality constraints to the driver.  However, for my actual problem it's hard to find an initial starting point that satisfy all the constraints, and as the result the optimizer failed to do anything.  I figure maybe I could define y and z as states in an implicit component and have a nonlinear solver figure out the right values of y and z given x, then feed x to the optimization driver.</p>
  
  <p>Is this a possible approach?  If so, how will the implicit component look like in this case?  I looked at the Sellar problem tutorial but I wasn't able to translate it to this case.</p>