I'm working on a Hybrid classical-quantum linear solver. For this, they make a loop on a quantum circuit (ie. below), and each time they change the value of the classical register and apply a X gate on the quantum register conditioned on the state of the classical register. 
Therefore, I ask myself, is there a way to initialize the classical register ?
Classical registers are typically used for capturing measurement results, and may also be used for conditionally applying quantum operation. See: https://github.com/Qiskit/openqasm/blob/master/spec/qasm2.rst
Given the problem you described, one approach would be to have a classical program that iteratively: 1) defines and executes a quantum circuit on a quantum processor or simulator 2) reads the results from the classical registers for guidance in defining the circuit for the next iteration
Here comes an illustration code written by myself.
from qiskit import QuantumRegister,ClassicalRegister,QuantumCircuit,Aer,execute
from qiskit.providers.aer import QasmSimulator
qr=QuantumRegister(1)
cr0=ClassicalRegister(5)
circ=QuantumCircuit(qr,cr0)
circ.measure(qr,cr0[0])
circ.x(qr)
circ.measure(qr,cr0[2])
circ.measure(qr,cr0[3])
circ.x(qr)
circ.measure(qr,cr0[3])
circ.x(qr)
circ.measure(qr,cr0[4])
circ.h(qr)
circ.x(qr)
print(execute(circ,Aer.get_backend('qasm_simulator')).result().get_counts())
The upper code shows how to get varied values and assign them to different classical registers. Although this method still requires a qubit, at least it can save some time. Maybe you can use the partial trace method to improve this. I think you must be ok with how the c_if() function works.
You might find this section of the documentation helpful, it goes over initializing and using registers.
https://qiskit.org/documentation/terra/quantum_circuits.html
