This is from an optimization and convex analysis class #7) Show that \( f(\cdot) \) is a convex function if and only if \(\text{epi}(f) \subseteq \mathbb{R}^{n+1}\) is a convex set.Let us denote all lsc, convex, proper functions by \(\mathcal{F}\).

Kindly refer to Step 2 for the solution.

Answered: #7) Show that f(-) is a convex function…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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#7) Show that f(-) is a convex function if and only if epi(f) C R"+¹ is a convex set. Let us denote all lsc, convex, proper functions by F.