Seminar: On the Subdifferential of the Value Function for Parametric Generalized Polyhedral Convex Optimization Problems

Thời gian: 14:00 đến 15:30 Ngày 19/05/2026

Địa điểm: Phòng C101, VIASM

Báo cáo viên: PGS. TS. Nguyễn Ngọc Luân, Trường Đại học Sư phạm Hà Nội

Tóm tắt: This talk investigates the differential stability of convex optimization problems within the framework Banach spaces. We focus specifically on structures defined by generalized polyhedral convex sets and functions. First, a computation formula for the normal cone to the intersection of two generalized polyhedral convex sets is established. Based on this geometric result, we derive calculus rules for the subdifferential and singular subdifferential of the sum of two functions, dispensing with the standard continuity assumptions typically required in convex analysis. These tools are subsequently applied to analyze parametric optimization problems, yielding exact formulas for the subdifferential and singular subdifferential of the optimal value function. Notably, our results refine recent findings in the literature by demonstrating that certain previously established upper estimates are, in fact, equalities.