# Disjunctive program

In its most general form, this seeks a solution to one of a finite list of mathematical programs:

$LaTeX: x^* \in \mbox{argopt} \{f_k(x): x \in X_k \}$,

for some $LaTeX: k=1,...,K$. Usually, they have the same objective functions, $LaTeX: f_k=f$ for all $LaTeX: k$, so the mathematical program with disjunctive constraints has the following form:

$LaTeX: \mbox{opt} \left\{ f(x): x \in X, \left(g_1(x) \le 0 \mbox{ or } g_2(x) \le 0 \mbox{ or } \ldots \mbox{ or } g_k(x) \le 0 \right) \right\}$.

This can be reformulated as a mixed-integer program, using binary variables to represent the disjunction.