F. Flores-Bazan, F. Thiele
This paper provides sufficient conditions ensuring the lower semicontinuity of the value function associated to a quasiconvex minimization problem under inequality constraints. In some situations, our conditions will imply also the existence of solutions. In convex optimization, it is known that zero duality gap is equivalent to the lower semicontinuity of such a value function at the origin. Here, the dual problem is defined in terms of the linear Langrangian. Thus, our results may be viewed as extensions of the latter for classes of nonconvex optimization problems. Several examples showing the applicability of our approach and the non applicability of any other result elsewhere, are exhibited. Furthermore, we identify a suitable large class of functions (quadratic-linear fractional) to which the involved functions could belong to and our results apply.
Keywords: Zero duality gap, Lagrangian duality, quasiconvex programming, nonconvex quadratic programming
Scheduled
GT11 Continuous Optimization II
June 9, 2022 12:00 PM
A12
