Use os SOS2 in Linear Optimization

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I have a linear optimization to minimize value like

MIN = sum(x_i*j_i)
 Constrains:
        0 < x_i  < C
        0 < j_i < J
        x_i + y_i <= x_(i-1) + f(x_i)

Where this f(x_i) is a SOS2 function:

Sum(lambda_i) = 1
Sum(lambda_i * X_i) = x_i  # Here X_i is a constant.
Sum(lambda_i * K_i) = result # Here K_i is a constant. 
this result will be returned.

When I make individual MixedIntegerLinearProgram(maximization=False, solver = "GLPK") one for f(x), I am able to slove. When introducing the function as another variable into another MixedIntegerLinearProgram(maximization=False, solver = "GLPK") I am unable to get the results.

Need help in actually formulating the sage equations.