如何使用GEKKO对日志或sqrt建模？ 约束

Question

I'm trying to develop my constraints with GEKKO, and I need to include some mathematical operations as log, coth or sqrt.

I tried initially with my habitual procedures, using numpy or mpmath, but I figure out that using GEKKO I need to use their operator definitions, as m.wathever (log,...), once the m = GEKKO() is done

How is the best way to develop that? Should I take some considerations while I'm changing it?

K_t = (1 + m + np.sqrt(1 + m**3)) - mpmath.coth(s/2)  # Ref 2. Same results

Answer 1

Use the Gekko versions of those functions instead of the NumPy or Math versions:

gk = GEKKO()
K_t = (1 + m + gk.sqrt(1 + m**3)) - gk.cosh(s/2)/gk.sinh(s/2)

The Gekko versions are needed because of operator overloading to calculate first and second derivatives for the solvers with automatic differentiation. There is no coth so you'll need to substitute with coth(x) = cosh(x)/sinh(x) . I typically define my Gekko model as m=GEKKO() but you have another variable named m so I used gk instead. Here is a section from the documentation on Model Building Functions .

Equation Functions

Special function besides algebraic operators are available through GEKKO functions. These must be used (not numpy or other equivalent functions):

• gk.sin(other)
• gk.cos(other)
• gk.tan(other)
• gk.asin(other)
• gk.acos(other)
• gk.atan(other)
• gk.sinh(other)
• gk.cosh(other)
• gk.tanh(other)
• gk.exp(other)
• gk.log(other)
• gk.log10(other)
• gk.sqrt(other)