title: Problem solving a minimization problem in cvxpy
body: <p>I have a linear optimization problem, which can be expressed in a cost function code like this:</p>
  
  <pre><code>value_to_minimize = 0.0;
  for i in range(0, len(v_1)):
      value_to_minimize += np.abs(v_1[i] - (v_2[i] * c1 + v_3[i] * c2 + v_4[i] * c3));
  </code></pre>
  
  <p>The task of the solver should be to find values for the variables <code>c1</code>, <code>c2</code>, <code>c3</code> which minimize the value.  As boundary conditions, <code>c1</code>, <code>c2</code>, <code>c3</code> together should result in 1.0 and not be negative.
  <code>v_1</code>, <code>v_2</code>, <code>v_3</code> and <code>v_4</code> are vectors with 10000 float values.</p>
  
  <p>Here is the outline to solve this minimization problem in cvxpy, but without the parameter pass in cp.Minimize(...):</p>
  
  <pre><code>V1 = np.array(v_1).reshape(10000, 1)
  V2 = np.array(v_2 + v_3 + v_4).reshape(10000, 3)
  c = cp.Variable((3,1),nonneg=True)
  
  prob = cp.Problem(cp.Minimize(..., # ???
                  [sum(c) == 1])) 
  prob.solve(verbose=True)
  </code></pre>
  
  <p>How would the minimize function for cvxpy look in that case?</p>