QUBO and PUBO format output #143
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termoshtt
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Nov 15, 2024
…#144) # Summary - Add optional fields, `dual_variable` and `penalty_weight` in `Constraint` message. - This will be used in #143 to create unconstrained problem. #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.
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to_quboandto_puboto create Quadratic Unconstrained Binary Optimization (QUBO) and Polynomial ... (PUBO) formats.