On checking unboundedness of functions

Abstract EN

While solving a minimization problem, an important mathematical issue is to check whether the objective function is unbounded below on the set of feasible solutions.

In linear and convex quadratic programming problems this issue is well resolved in the sense that there are efficient methods to do it in those problems; in fact when the objective function is unbounded below, these methods provide a half-line in the set of feasible solutions along which it diverges to-We discuss how unboundedness can be checked in other nonlinear programming problems.