I have a "linear" equation set as follows, with nonlinear optimization goal.
P(0) + P(1) = 1
P(0, 0) + P(0,1) = P(0)
P(0) < 1
P(1) < 1
P(0,0) > 0
P(0,1) > 0
P(1) > 0
The goal to optimize is
$P(0,1)\log{P(0,1)} + P(1)\log{P(1)} - (P(1)+P(0,1))\log{((P(1)+P(0,1)))}$
I know nonlinear optimization could be hard, but is there quick technique dor solving this special kind of nonlinear optimization problem?