The following equation and associated level values are provided as an example:Nonlinear equations are treated differently. If the coefficient of a variable in the equation listing is enclosed in parentheses, then the corresponding constraint is nonlinear, and the value of the coefficient depends on the activity levels of one or more of the variables. The listing is not algebraic, but shows the partial derivative of each variable evaluated at their current level values.
and the equation appears in the Equation Listing as:eq1.. 2*sqr(x)*power(y,3) + 5*x - 1.5/y =e= 2; x.l = 2; y.l = 3 ;
I'll denote by f(x,y) = 2*x^2*y^3 + 5*x - 1.5/y the nonlinear function in question.eq1.. (221)*x + (216.1667)*y =E= 2 ; (LHS = 225.5 ***)
I understand that the values 221 and 216.1667 are the partial derivative of f with respect to x and y, respectively, evaluated in the point (x,y)=(2,3). However, it is not clear to me what the function 221*x + 216.1667*y has to do with the original function f.
The linearisation of f around the point (x,y)=(2,3) is given by
f(2,3) + f_x(2,3) * (x-2) + f_y(2,3) * (y-3)
(where f_x denotes the partial derivative of f w.r.t. x) which evaluates to
225.5 + 221 * (x-2) + 216.1667 * (y-3)
(Incidentally, plugging in (x,y)=(2,3) gives 225.5, which is mentioned above as the LHS value.)
If the output is meant to represent the linearisation, why does it read
instead of, for example,eq1.. (221)*x + (216.1667)*y =E= 2 ; (LHS = 225.5 ***)
225.5 + 221 * (x-2) + 216.1667 * (y-3) =E= 2
Is it just confusing for no reason, or is there a deeper meaning?