Solving Disjunctive Optimization Problems by Generalized Semi-infinite Optimization Techniques

We describe a new possibility to model disjunctive optimization problems as generalized semi‐infinite programs. In contrast to existing methods in disjunctive programming, our approach does not expect any special formulation of the underlying logical expression. Applying existing lower‐level reformulations for the corresponding semi‐infinite program, we derive conjunctive nonlinear problems without any logical expressions, which can be locally solved by standard nonlinear solvers. Our preliminary numerical results on some small‐scale examples indicate that our reformulation procedure is a reasonable method to solve disjunctive optimization problems.