quadprog

import numpy as np from quadprog import solve_qp # Define the quadratic program: # Minimize 0.5 * x^T G x + a^T x # Subject to C^T x >= b # Example: Minimize x^2 + y^2 - x - y # This means G = [[2, 0], [0, 2]] and a = [-1, -1] G = np.array([[2., 0.], [0., 2.]]) a = np.array([-1., -1.]) # Constraints: x >= 0, y >= 0, x + y >= 1 # In quadprog, C's columns are the normal vectors of the constraints. # C^T x >= b => [[1, 0, 1], [0, 1, 1]]^T x >= [0, 0, 1]^T # Which means: # 1*x + 0*y >= 0 # 0*x + 1*y >= 0 # 1*x + 1*y >= 1 C = np.array([[1., 0., 1.], [0., 1., 1.]]) b = np.array([0., 0., 1.]) # Number of equality constraints (first 'meq' rows of C and b) meq = 0 # Solve the QP. It returns (x, fval, xu, l) # x: solution vector # fval: objective function value at x # xu: unconstrained solution (unused in this example) # l: Lagrange multipliers (unused in this example) solution, _, _, _ = solve_qp(G, a, C, b, meq) print(f"Optimal solution x: {solution}") # Expected output for this problem: Optimal solution x: [0.5 0.5]