Speaker：Jane J.Ye (University of Victoria)

Time：2025-3-13, 16:30

Location：Conference Room C503 at Administration Building at Haiyun Campus 

Abstract:

In this talk we present some new second-order optimality conditions for a very general set-constrained optimization problem where the underlying set may be nononvex. Utilizing the classical and/or the lower generalized support function, we obtain new second-order necessary and sufficient conditions via both the corresponding asymptotic second-order tangent cone and outer second-order tangent set. Our necessary optimality conditions do not require convexity and/or nonemptiness of the second-order tangent set and our sufficient conditions do not require convexity and/or nonemptiness of the second-order tangent set and the second-order regularity of the underlying set as required in the classical result. These are important improvements to the classical results in the literature since the second-order tangent set can be nonconvex and empty even when the set is convex and the second-order regularity is a very difficult condition to check.