Decogo
Decogo is a software framework for decomposition-based global optimization of block-separable MINLP problems of the form
\begin{equation}
\min \, c^Tx : x\in P,\,\, x_k\in X_k,\,\, k\in K
\end{equation}
with
\begin{equation}
P:= \{x \in {\bf R}^{n}: \, \, a_i^T x\leq b_i,\, i\in M_1,
\,\, a_i^T x= b_i,\, i\in M_2 \},
\end{equation}
\(|M_1|+|M_2|=m\), and
\begin{equation}
X_k:=\{ y \in [\underline{x}_k, \overline{x}_k] \subset {\bf R}^{n_{k1}}
\times {\bf Z}^{n_{k2}}: g_{kj}(y)\leq 0,\, j\in J_k \}.
\end{equation}
The vector of variables \(x \in {\bf R}^n\) is partitioned into \(|K|\) blocks such that \(n=\sum\limits_{k \in K}n_k\), where \(n_k=n_{k1}+n_{k2}\) is the dimension of block \(k\), \(n=\sum\limits_{k \in K}n_k\) and \(x_k\in {\bf R}^{n_k}\) denotes the variables of block \(k\). The vectors \(\underline{x}, \overline{x} \in {\bf R}^{n}\) denote lower and upper bounds on the variables.
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