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Problems minimizing an overconstrained system


I'm getting problems using FindMinimum when there are multiple active
constraints at the minimum point. Here's a test case that demonstrates
this problem

FindMinimum[{Max[p[1], p[3]],
 p[1] + p[2] + p[3] == 1 && 1/10 <= p[3] <= 4/5 && p[1] == 4/5 &&
  p[2] == 1/10}, {p[1], p[2], p[3]}]

fails with " There are no points that satisfy the constraints", while
different objective function with the same constraints works --

FindMinimum[{p[1] + p[3],
 p[1] + p[2] + p[3] == 1 && 1/10 <= p[3] <= 4/5 && p[1] == 4/5 &&
  p[2] == 1/10}, {p[1], p[2], p[3]}]

Is there any way around this behavior?

Yaroslav



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