Python中Gurobi矩阵变量约束索引的维度兼容问题求助

Let's walk through the key issues in your code that are causing the dimension mismatch, and fix them step by step:

• Incorrect initialization of Bu
  You wrote Bu=np.array((3,4)), which creates a 1D array with two elements [3,4], not a 3×4 matrix as you intended. You need to initialize it as a proper 3-row, 4-column matrix. For example:

  Bu = np.random.rand(3,4)  # Replace with your actual values
  

• Misplaced s1 variable definition
  You're defining s1 = m.addMVar((3,N)) inside the second loop (for i in range(N+1,7)), which means you're creating a new 3×5 variable matrix every iteration. This is unnecessary and can cause confusion with variable scoping. Move this line outside the loop so it's created once.

• Dimension mismatch in constraint expressions
  The left-hand side (LHS) of your constraint is a 3×1 numpy array, while the right-hand side (RHS) has a 1D MVar slice (s1[:,k]). Gurobi's MVar slices return 1D objects by default, so we need to reshape s1[:,k] to a 3×1 column vector to match the LHS dimension. Additionally, ensure that all matrix multiplications result in compatible shapes:

  • dDelta is a 4×4 diagonal matrix (from deltaBut, a 4×1 array)
  • Bu@dDelta gives a 3×4 matrix, which when multiplied by useq[i-k-2] (4×1) gives a 3×1 vector
  • Ts*np.linalg.inv(M)@(Bu@dDelta@useq[i-k-2]) will correctly be a 3×1 vector

• Missing parentheses in m.optimize()
  You have m.optimize instead of m.optimize() — this won't actually run the optimization.

Fixed Full Code #

import gurobipy as gp
import numpy as np

N = 5
m = gp.Model("matrix")
Ts = 0.2
M = np.eye(3)
D = np.eye(3)
C = np.eye(3)
# Fix: Initialize Bu as a proper 3x4 matrix
Bu = np.random.rand(3,4)  # Replace with your actual values
pos = np.array([0,0,0]).reshape(3,1)  # Ensure it's a column vector (3x1)
u = np.array([0,0,0,0]).reshape(4,1)  # Ensure it's a column vector (4x1)
xseq = []
xseq.append(pos)
useq = []

# 1st loop: Populate initial sequences
for i in range(1, N+1):
    xseq.append(pos)
    useq.append(u)

# Fix: Define s1 once outside the loop
s1 = m.addMVar((3, N))  # 3x5 matrix variable
obj1 = 0

# 2nd loop
for i in range(N+1, 7):
    A = np.eye(3)
    # Create deltaBut variables as a 4x1 MVar instead of individual vars (cleaner)
    deltaBut = m.addMVar((4,1))
    dDelta = np.diag(deltaBut.flatten())  # Convert to 4x4 diagonal matrix
    
    for k in range(0, N):
        # Calculate RHS components with correct dimensions
        rhs_part = Ts * np.linalg.inv(M) @ Bu @ dDelta @ useq[i-k-2]
        # Reshape s1[:,k] to 3x1 to match LHS dimension
        m.addConstr(xseq[i-k-1] - A @ xseq[i-k-2] == rhs_part + s1[:,k].reshape(3,1))
        # Update objective with quadratic term
        obj1 += s1[:,k] @ s1[:,k]

# Set objective and optimize
m.setObjective(10**3 * obj1, gp.GRB.MINIMIZE)  # Specify minimization (optional but clear)
m.optimize()

Additional Notes #

• I changed how deltaBut is created: using m.addMVar((4,1)) is cleaner than creating four individual variables and combining them into an array.
• Ensured pos and u are initialized as column vectors (3x1 and 4x1) to avoid unintended 1D array behavior during matrix multiplication.
• Added gp.GRB.MINIMIZE to the objective for clarity (Gurobi defaults to minimization, but it's good practice to specify).

内容的提问来源于stack exchange，提问作者waseem Khan