Apply ADMM to the program

[SikangSHU]

Hello! I'd like to apply ADMM to my program so that the speed of the algorithm can be improved. Can I use ADMM to decide which stain vector matrix is the best for each pixel when doing stain unmixing for 4 colours? Is the framework as follows available when solving whole slide image? Any suggestion will be OK. Thank you!

from numpy import linalg
from docplex.mp.model import Model

from qiskit import BasicAer
from qiskit.aqua.algorithms import QAOA, NumPyMinimumEigensolver
from qiskit.optimization.algorithms import CobylaOptimizer, MinimumEigenOptimizer
from qiskit.optimization.problems import QuadraticProgram
from qiskit.optimization.algorithms.admm_optimizer import ADMMParameters, ADMMOptimizer
import pyvips
import gc

image = pyvips.Image.tiffload('E:\\unc.ome.tif')

image = image.colourspace("scrgb")

stain_vectors_1 = [
    [0.571, 0.095, 0.767],
    [0.584, 0.258, 0.576],
    [0.577, 0.961, 0.284]
]
stain_inverse_1 = linalg.inv(stain_vectors_1).tolist()
stain_space_1 = image.recomb(stain_inverse_1)

stain_vectors_2 = [
    [0.095, 0.105, 0.767],
    [0.258, 0.758, 0.576],
    [0.961, 0.644, 0.284]
]
stain_inverse_2 = linalg.inv(stain_vectors_2).tolist()
stain_space_2 = image.recomb(stain_inverse_2)

stain_vectors_3 = [
    [0.571, 0.767, -0.48],
    [0.584, 0.576, 0.808],
    [0.577, 0.284, -0.343]
]
stain_inverse_3 = linalg.inv(stain_vectors_3).tolist()
stain_space_3 = image.recomb(stain_inverse_3)

stain_vectors_4 = [
    [0.095, 0.767, -0.553],
    [0.258, 0.576, 0.817],
    [0.961, 0.284, -0.165]
]
stain_inverse_4 = linalg.inv(stain_vectors_4).tolist()
stain_space_4 = image.recomb(stain_inverse_4)

stain_vectors_5 = [
    [0.105, 0.767, -0.218],
    [0.758, 0.576, 0.649],
    [0.644, 0.284, -0.729]
]
stain_inverse_5 = linalg.inv(stain_vectors_5).tolist()
stain_space_5 = image.recomb(stain_inverse_5)

# define COBYLA optimizer to handle convex continuous problems.
cobyla = CobylaOptimizer()

# define QAOA via the minimum eigen optimizer
qaoa = MinimumEigenOptimizer(QAOA(quantum_instance=BasicAer.get_backend('statevector_simulator')))

# exact QUBO solver as classical benchmark
exact = MinimumEigenOptimizer(NumPyMinimumEigensolver()) # to solve QUBOs

# in case CPLEX is installed it can also be used for the convex problems, the QUBO,
# or as a benchmark for the full problem.
#
# cplex = CplexOptimizer()

mdl = Model('stain_unmixing')

mdl.minimize(。。。)
mdl.add_constraint(。。。)

qp = QuadraticProgram()
qp.from_docplex(mdl)
print(qp.export_as_lp_string())

admm_params = ADMMParameters(
                            rho_initial=1001,
                            beta=1000,
                            factor_c=900,
                            maxiter=100,
                            three_block=True, tol=1.e-6
                        )

# define QUBO optimizer
qubo_optimizer = exact
# qubo_optimizer = cplex  # uncomment to use CPLEX instead

# define classical optimizer
convex_optimizer = cobyla
# convex_optimizer = cplex  # uncomment to use CPLEX instead

# initialize ADMM with classical QUBO and convex optimizer
admm = ADMMOptimizer(params=admm_params,
                     qubo_optimizer=qubo_optimizer,
                     continuous_optimizer=convex_optimizer)

# run ADMM to solve problem
result = admm.solve(stain_unmixing)