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# The norm and penalty approximation problems of section 10.5 (Examples).
from cvxopt import normal, setseed
from cvxopt.modeling import variable, op, max, sum
setseed(0)
m, n = 500, 100
A = normal(m,n)
b = normal(m)
x1 = variable(n)
prob1=op(max(abs(A*x1+b)))
prob1.solve()
x2 = variable(n)
prob2=op(sum(abs(A*x2+b)))
prob2.solve()
x3 = variable(n)
prob3=op(sum(max(0, abs(A*x3+b)-0.75, 2*abs(A*x3+b)-2.25)))
prob3.solve()
try: import pylab
except ImportError: pass
else:
pylab.subplot(311)
pylab.hist(A*x1.value + b, m//5)
pylab.subplot(312)
pylab.hist(A*x2.value + b, m//5)
pylab.subplot(313)
pylab.hist(A*x3.value + b, m//5)
pylab.show()
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