Formulation of a multivariate piecewise linear constraints

Answered

Patrick Halder

May 12, 2023 12:36 Edited

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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)

 

Related to

• Piecewise Linear

0

• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  November 13, 2026 01:43

  This post is more than two 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 try Gurobot, our chatbot interface offering instant, expert-level support.
• 

  Riley Clement

  • Gurobi Staff

  May 14, 2023 11:42 Edited

  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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