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# The small LP of section 10.4 (Optimization problems).
from cvxopt import matrix
from cvxopt.modeling import variable, op, dot
x = variable()
y = variable()
c1 = ( 2*x+y <= 3 )
c2 = ( x+2*y <= 3 )
c3 = ( x >= 0 )
c4 = ( y >= 0 )
lp1 = op(-4*x-5*y, [c1,c2,c3,c4])
lp1.solve()
print("\nstatus: %s" %lp1.status)
print("optimal value: %f" %lp1.objective.value()[0])
print("optimal x: %f" %x.value[0])
print("optimal y: %f" %y.value[0])
print("optimal multiplier for 1st constraint: %f" %c1.multiplier.value[0])
print("optimal multiplier for 2nd constraint: %f" %c2.multiplier.value[0])
print("optimal multiplier for 3rd constraint: %f" %c3.multiplier.value[0])
print("optimal multiplier for 4th constraint: %f\n" %c4.multiplier.value[0])
x = variable(2)
A = matrix([[2.,1.,-1.,0.], [1.,2.,0.,-1.]])
b = matrix([3.,3.,0.,0.])
c = matrix([-4.,-5.])
ineq = ( A*x <= b )
lp2 = op(dot(c,x), ineq)
lp2.solve()
print("\nstatus: %s" %lp2.status)
print("optimal value: %f" %lp2.objective.value()[0])
print("optimal x: \n")
print(x.value)
print("optimal multiplier: \n")
print(ineq.multiplier.value)
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