Disjunctive program

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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.


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