Vectorizing addition of constraints

Carlos Martin

• June 11, 2020 23:59
• Edited

I'm using the Python API. Is there a vectorized way to add the following constraints?

model.addConstrs((
    v <= u[:, :, i] @ x
    for i in range(u.shape[2])
))

where v and x are MVars, e.g.

v.shape == (2,)
x.shape == (3,)
u.shape == (2, 3, 4)

This is a time-critical component of my program, but Python for loops are very slow and take up a lot of time.

0

• Official comment

  

  Simranjit Kaur

  Gurobi Staff

  • December 06, 2024 00:45

  This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum. Or why not try our AI Gurobot?.
• 

  Greg Glockner

  Gurobi Staff

  • June 12, 2020 00:15

  Unfortunately, no. However, the following may be more efficient for this model since it avoids some intermediate Python objects:

  for i in range(u.shape[2]):
    model.addMConstrs(u[:, :, i], x, '>', v)

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• 

  Carlos Martin

  • June 12, 2020 00:38

  

  

  

  @... That yields the following error:

  Traceback (most recent call last):
  ...
  model.addMConstrs(u[:, :, i], x, '>', v)
  File "model.pxi", line 3414, in gurobipy.Model.addMConstrs
  TypeError: object of type 'MVar' has no len()

   

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• 

  Carlos Martin

  • June 12, 2020 00:50
  • Edited

  

  

  

  More generally, are there plans to add a completely vectorized interface like that of cvxopt.solvers.lp (ideally with the addition of a batch dimension)? This would be extremely useful.

  Currently cvxopt.solvers.lp (with GLPK) is >6 times faster for me, simply due to model construction/specification overhead. (My program needs to solve a large batch of linear programs, which presently involves constructing and solving models repeatedly.)

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• 

  Robert Luce

  Gurobi Staff

  • June 12, 2020 09:12

  Hello Carlos,

  I have taken note of your request for an API to solve many small models in bulk. In order to understand the overhead problem you are facing a little better, it would be very valuable if you could post a concise benchmark example here that demonstrates the enourmous overhead w.r.t. cvxpy.solvers.lp/GLPK.

  Greg's suggestion from above won't work (as you saw...) because the RHS argument to addMConstrs must be a data vector, not an MVar object. You would need to normalize the constraint u[:,:.i] @ x >= v  to the form A @ z >= 0 yourself in order to go through this function, but I'm afraid the benefit will be quite small.

  Thanks,

  Robert

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• 

  Carlos Martin

  • June 12, 2020 21:42
  • Edited

  

  

  

  Robert Luce Here is an example: Solving batches of two-player zero-sum normal-form games. I get times like

  gurobi 0.37076228499999986
  cvxopt 0.009740684000000055
  
  gurobi 0.39596498599999985
  cvxopt 0.009115292999999802
  
  gurobi 0.3703212579999997
  cvxopt 0.007263605999999978

  when running on a 2.5 GHz Quad-Core Intel Core i7 processor with 16 GB 1600 MHz DDR3 memory.

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• 

  Carlos Martin

  • June 16, 2020 03:08
  • Edited

  

  

  

  I see there's a Feature Requests subforum, should I post this there?

  I suppose the ideal interface might look something like

  def max_min(batch):
      model = gurobipy.Model()
      v = model.addMVar(batch.shape[0])
      x = model.addMVar((batch.shape[0], batch.shape[1]))
      model.setObjective(v, gurobipy.GRB.MAXIMIZE)  # note this is vectorized
      model.addConstrs((
          x.sum(1) == 1,
          x >= 0,
          v[:, None] <= (batch * x[:, :, None]).sum(1),
      ))
      model.optimize()
      return model.objVal

  Alternatively, inputting batches of c, A, b, G, h matrices would work too.

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