title: How to fix local infeasibility in IPOPT with Python Gekko?
body: <p>I get a local infeasibility error in IPOPT (v3.12.10).</p>
  
  <pre><code>Converged to a point of local infeasibility. Problem may be infeasible.
  </code></pre>
  
  <p>I also tried it with the APOPT solver using <code>m.options.SOLVER=1</code> and get a similar error.</p>
  
  <pre><code>No feasible solution
  </code></pre>
  
  <p>There are multiple feasible solutions to this problem with two equations and three variables. Solutions to this problem are where the plane intersects the sphere.</p>
  
  <pre class="lang-py prettyprint-override"><code>from gekko import GEKKO
  m = GEKKO()
  x=m.Var(); y=m.Var(); z=m.Var()
  m.Equations([x**2+y**2+z**2==1,x+z==y])
  m.options.SOLVER = 3 # APOPT=1, IPOPT=3
  m.solve(debug=0) # debug=0 doesn't stop when unsuccessful
  print('Solution 1')
  print(x.value[0],y.value[0],z.value[0])
  </code></pre>
  
  <p>When I add an objective function to maximize <code>z</code> then IPOPT converges to a solution.</p>
  
  <pre class="lang-py prettyprint-override"><code># add objective
  m.Obj(-z) # maximize z
  m.solve()
  print('Solution 2')
  print(x.value[0],y.value[0],z.value[0])
  </code></pre>
  
  <p>How can I avoid a failed solution without adding an objective function?</p>