More examples for optimization subject to inequality constraints, Kuhn-Tucker
Example for optimization subject to a single constraint such that imposing the constraint as an equality implies a negative Lagrange multiplier, and imposing the same constraint as an inequality implies a positive Lagrange multiplier.
Note that I'm not checking constraint qualification in this video, even though one should. Check that this is not a problem in this case, since the point where constraint qualification does not hold is not a maximum.
Errata: At 19:21 in grad f = \lambda grad g, I forgot to write down grad g. At 27:22, the second entry in the gradient of g is 2y+5, not 2y+1. At 34:23 and in the following, it is y_1,2 = 5/2 +/ sqrt(752)/10, not /100.