Solving Disjunctive Optimization Problems by Generalized Semi-infinite Optimization Techniques

Abstract

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.

Optimality Conditions for Convex Semi-infinite Programming Problems with Finitely Representable Compact Index Sets

“…(3) 155 Then, given x ∈ X , the first and the second order necessary optimality conditions for 156t ∈ T * in the problem (LLP(x)) can be formulated in terms of functions (3), as follows…”