  Mathematical programs with or-constraints form a new class of disjunctive
optimization problems with inherent practical relevance. In this paper, we
provide a comparison of three different first-order methods for the numerical
treatment of this problem class which are inspired by classical approaches from
disjunctive programming. First, we study the replacement of the or-constraints
as nonlinear inequality constraints using suitable NCP-functions. Second, we
transfer the or-constrained program into a mathematical program with switching
or complementarity constraints which can be treated with the aid of well-known
relaxation methods. Third, a direct Scholtes-type relaxation of the
or-constraints is investigated. A numerical comparison of all these approaches
which is based on three essentially different model programs from
or-constrained optimization closes the paper.
