Formulation of a multivariate piecewise linear constraints

回答済み

Patrick Halder

2023年05月12日 12:36 編集済み

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I have the following problem:

How can I model the function p(y) and use it within my big-M constraint with Gurobi in Python?

I already have something like this, but the solution of the model seems to be incorrect:

eps = 0.0001
M1 = 10000 + eps
M2 = 10000

for subspace in subspaces:
 z_binaries = []
 for hyperplane in subspace:
  z_bin = self.model.addVar(vtype=GRB.BINARY)
  append(z_bin)

  A = LinExpr(hyperplane.a + [-M1], y + [z_bin])
  rhs = hyperplane.b - M1
  model.addLConstr(A, GRB.GREATER_EQUAL, rhs)

  rhs2 = hyperplane.b
  model.addLConstr(A, GRB.LESS_EQUAL, rhs2)

 delta = model.addVar(vtype=GRB.INTEGER)
 model.addGenConstrAnd(delta, z_binaries)

A = LinExpr(subspace.a + [-M2, -1.0], y + [z] + [r])
rhs = subspace.b - M2
model.addGenConstrIndicator(delta, True, A, GRB.GREATER_EQUAL, rhs)

 

関連

• Piecewise Linear

0

• 

  Riley Clement

  • Gurobi Staff

  2023年05月14日 11:42 編集済み

  Hi Patrick,

  One approach would be to construct m disjoint convex regions:

  \[\mathcal{S}'_i = \{(p,y) : y \in \mathcal{S}_i, p = a^T_i - b_i\}\]

  over completely separate sets of variables, eg \((p_i, y_i)\), then introduce binary variables \(x_1, \ldots, x_m\) and the constraint \(\sum_i x_i = 1\)

  and use indicator constraints of the form

  (x_i == 1) >> (p == p_i)

  (or the big M equivalent).

  - Riley

   

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