From eb4bb1e940b223d9c508733aaa3700701f51e986 Mon Sep 17 00:00:00 2001 From: Christian Grothoff Date: Thu, 13 Sep 2018 17:44:03 +0200 Subject: fix build --- coinselection/ilp.tex | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) (limited to 'coinselection/ilp.tex') diff --git a/coinselection/ilp.tex b/coinselection/ilp.tex index b182000..5d65ae5 100644 --- a/coinselection/ilp.tex +++ b/coinselection/ilp.tex @@ -59,7 +59,7 @@ Simple model: - \sum_{c \in {\cal C}} n_c \cdot \alpha \\ \texttt{such that} \quad \bigwedge_{c \in {\cal C}} n_c \cdot (d_c + f^{withdraw}_c) &\le w \label{eq:sound} \\ - n_c &\in {\mathbb N_0} \label{eq:nc} + n_c &\in {\mathbb N}_0 \label{eq:nc} \end{align} Explanations: @@ -112,7 +112,7 @@ and then study the affect on larger simulations of many transactions. \begin{align} \min &M \cdot \tau + \sum_{c \in {\cal C}} s_c - + \sum_{c \in {\cal C}} n_c \cdot \alpha) + + \sum_{c \in {\cal C}} n_c \cdot \alpha + \sum_{c \in {\cal C}} r_c \cdot \beta \\ \texttt{such that} \quad \bigwedge_{c \in {\cal C}} n_c \cdot d_c &\ge s_c \label{eq:coinnum} \\ @@ -121,10 +121,10 @@ and then study the affect on larger simulations of many transactions. \sum_{c \in {\cal C}} (s_c - f^{deposit}_c \cdot n_c) + f &\ge p \label{eq:fees} \\ \sum_{c \in {\cal C}} s_c - \tau p &\le p \label{eq:tau} \\ \tau &\in \{0,1\} \label{eq:bin} \\ - n_c &\in {\mathbb N_0} \label{eq:nc} \\ - s_c &\in {\mathbb R^+_0} \label{eq:r} \\ - r_c \cdot d_c + sc_c \ge n_c \cdot d_c \label{eq:refresh} \\ - r_c &\in \{0,1\}_ \label{eq:rc} + n_c &\in {\mathbb N}_0 \label{eq:nc} \\ + s_c &\in {\mathbb R}^+_0 \label{eq:r} \\ + r_c \cdot d_c + s_c &\ge n_c \cdot d_c \label{eq:refresh} \\ + r_c &\in \{0,1\} \label{eq:rc} \end{align} Explanations: -- cgit v1.2.3