PuLP目标函数中ABS()的数学运算

Question

I am trying to build a LP problem in PuLP and since I am new to python, wanted to know how to write the objective function with the operation of absolute values.

Till now I was using AMPL for my problem formulation and now want to convert the whole model to Python. Can anyone help me understand how to code

SUM(ABS(x)) in objective function of PulP
x is the decision variable which is output of the model and objective function of the model is SUM(ABS(x))

Answer 1

from pulp import *

N = 3
x_vars = LpVariable.dicts("x",range(N))
x_vars_abs = LpVariable.dicts("x_abs",range(N))
prob = LpProblem("min_sum_abs", LpMinimize)

# OBJECTIVE
prob += lpSum(x_vars_abs)

# ABS CONSTRAINTS
for i in range(N):
    prob += x_vars_abs[i] >= x_vars[i]
    prob += x_vars_abs[i] >= -x_vars[i]

# OTHER MODEL CONSTRAINTS
prob += lpSum(x_vars) >= 2.0
prob += x_vars[0] >= x_vars[1] + 1.0
prob += x_vars[1] <= x_vars[2] - 2.0

prob.solve()

print ("Status: " + str(LpStatus[prob.status]))
print ("Objective: " + str(value(prob.objective)))

for v in prob.variables():
    print (v.name + " = " + str(v.varValue))

Returns:

Status: Optimal
Objective: 2.6666667
x_0 = 0.66666667
x_1 = -0.33333333
x_2 = 1.6666667
x_abs_0 = 0.66666667
x_abs_1 = 0.33333333
x_abs_2 = 1.6666667