Dual example.md

Dual example

POLab
2017/10/30
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● 題目

● 主問題及對偶問題

Import gurobipy

from gurobipy import*

Model

m=Model('Dual example')

Add parameters

I=2
J=3
v=[3,5]
p=[[1,0,3],[0,2,2]]
a=[4,12,18]

Add decision variables

x={}
for i in range(I):
    x[i]=m.addVar(lb=0,vtype=GRB.CONTINUOUS,name='x_%d'%i)

Update

m.update()

Add objective and constraints

m.setObjective(quicksum(v[i]*x[i] for i in range(I)),GRB.MAXIMIZE)

for j in range(J):
    m.addConstr(quicksum(p[i][j]*x[i] for i in range(I))<=a[j],name='c%d'%j)

Result

m.optimize()
print('obj:%d'%m.objVal)
for v in m.getVars():
    print('%s:%d'%(v.varName,v.x))

Optimize a model with 3 rows, 2 columns and 4 nonzeros
Coefficient statistics:
  Matrix range     [1e+00, 3e+00]
  Objective range  [3e+00, 5e+00]
  Bounds range     [0e+00, 0e+00]
  RHS range        [4e+00, 2e+01]
Presolve removed 2 rows and 0 columns
Presolve time: 0.01s
Presolved: 1 rows, 2 columns, 2 nonzeros

Iteration    Objective       Primal Inf.    Dual Inf.      Time
       0    4.2000000e+01   1.500000e+00   0.000000e+00      0s
       1    3.6000000e+01   0.000000e+00   0.000000e+00      0s

Solved in 1 iterations and 0.01 seconds
Optimal objective  3.600000000e+01
obj:36
x_0:2
x_1:6

Get dual value

#透過限制式中的屬性pi取得對偶值
for c in m.getConstrs():
    print 'The dual value of %s : %g'%(c.constrName,c.pi)

The dual value of c0 : 0
The dual value of c1 : 1.5
The dual value of c2 : 1