id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ma-361	Evans, Mogoi N.; Moraa, Priscah	Nonlinear Geometry of Norm-Attaining Functionals: Variational Principles, Subdifferential Calculus, and Polynomial Optimization in Locally Convex Spaces	2025	11	.pdf	application/pdf	3670	258	54	For any continuous quasilinear p : X → R, there exists f ∈ X∗ attaining its p-norm and separating A from B: sup a∈A f (a) ≤ inf b∈B f (b) Proof. B−K.By the nonlinear separation theorem (see [1]), there exists f ∈ X∗ with: sup k∈K f (k) ≤ inf b∈B f (b) Step 3: Norm-Attainment VerificationThe critical observation is that f attains its p-norm on ∂K: ∃x0 ∈ ∂K with f (x0)	cache/ma-361.pdf	txt/ma-361.txt