dual_variable and penalty_weight in Constraint message for QUBO

[termoshtt]

Summary

• Add optional fields, dual_variable and penalty_weight in Constraint message.
• This will be used in QUBO and PUBO format output #143 to create unconstrained problem. QUBO and PUBO format output #143 will support two way to create QUBO and PUBO, penalty method and augmented Lagrangian method

Detail

For a problem

$$ \begin{align*} \min & f(x) \\ \text{s.t.} & g(x) = 0 \end{align*} $$

• Penalty method try to minimize $f(x) + \rho |g(x)|^2$, where $\rho$ is called penalty weight.
• Augmented Lagrangian method try to minimize $f(x) + \lambda g(x) + \rho |g(x)|^2$, where $\lambda$ is current dual variable and $\rho$ is also a penalty weight.

dual_variable field is intended to store $\lambda$, and penalty_weight stores $\rho$ in this sense.