Simple linear program with PuLP

Dockerfile

FROM ubuntu:16.04
MAINTAINER Paul Chaignon <paul.chaignon@gmail.com>

RUN apt update
RUN apt install -y python-pip glpk-utils coinor-cbc
RUN pip install pulp
RUN apt build-dep -y python-matplotlib
RUN pip install --no-cache-dir pylab

ADD . /lp
WORKDIR /lp

ENTRYPOINT python pl.py

pl.py

#!/usr/bin/env python
import pulp
from matplotlib.pylab import dot, random

def solve_minmax(n, a, b, x_min=None, x_max=None):
  x = pulp.LpVariable.dicts("x", range(n), x_min, x_max)
  m = pulp.LpVariable("m")
  lp_prob = pulp.LpProblem("Minmax Problem", pulp.LpMinimize)
  lp_prob += pulp.lpSum([m]), "Minimize_the_maximum"

  for i in range(n):
    label = "Max_constraint_%d" % i
    dot_b_x = pulp.lpSum([b[i][j] * x[j] for j in range(n)])
    condition = pulp.lpSum([m]) >= a[i] + dot_b_x
    lp_prob += condition, label

  lp_prob.writeLP("/tmp/MinmaxProblem.lp")  # optional
  lp_prob.solve(pulp.COIN_CMD())

  print "Status:", pulp.LpStatus[lp_prob.status]
  for v in lp_prob.variables():
    print v.name, "=", v.varValue
  print "Total Cost =", pulp.value(m)

if __name__ == "__main__":
  n = 50
  a = 2. * random(n) - 1.
  b = 2. * random((n, n)) - 1.
  solve_minmax(n, a, b, -5, 5)