1.
I want minimize_constrained()) to return a point such that the sum of
its coordinates is <= 1, in order to make the constraint c_5 positive. (The
docs [0] say that the constraints "should be either a function or list of
functions that must be positive.") However, the returned point's
coordinates sum to more than 1, and the point yields a negative number on
c_5. What am I doing wrong?
Here's a transcript of my session with Sage 7.5.1 on macOS Sierra:
sage: vars=var('x y')
sage:
f=-.2*log(1+1.1*x+4*y)-0.3*log(1+1.1*x-2*y)+0.2*log(1-x+4*y)-0.3*log(1-x-2*y)
sage: c_1 = lambda p: p[0]
sage: c_2 = lambda p: p[1]
sage: c_3 = lambda p: -p[0] + 1
sage: c_4 = lambda p: -p[1] + 1
sage: c_5 = lambda p: -p[0] -p[1] + 1
sage: minimize_constrained(f, [c_1, c_2, c_3, c_4, c_5], [0, 0])
(0.9999292893218813, 0.9999292893218813)
sage: c_5([0.9999292893218813, 0.9999292893218813])
-0.999858578643763
[0]
http://doc.sagemath.org/html/en/reference/numerical/sage/numerical/optimize.html
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