3 papers
math.OC2025
Exact penalty functions in optimization with unbounded constraint sets
Liguo Jiao, Tien-Son Pham, Nguyen Van Tuyen
This paper identifies necessary and sufficient conditions for the exactness of penalty functions in optimization problems whose constraint sets are not necessarily bounded. The cas…
math.AP2021
The mountain pass theorem in terms of tangencies
Si Tiep Dinh, Tien Son Pham
This paper addresses the Mountain Pass Theorem for locally Lipschitz functions on finite-dimensional vector spaces in terms of tangencies. Namely, let $f \colon \mathbb R^n \to \ma…
math.OC2020
Stability of closedness of closed convex sets under linear mappings
Si Tiep Dinh, Tien Son Pham
We study the problem of when the continuous linear image of a fixed closed convex set is closed. Specifically, we improve the main results in the papers \ci…