Convex Optimization · Problem 2.6

Convex functions — Boyd & Vandenberghe

Mathematics — Optimization · halfspace-containment

Problem

When does one halfspace contain another? Give conditions under which {x∣aTx≤b}⊆{x∣a~Tx≤b~}\{x \mid a^T x \leq b\} \subseteq \{x \mid \tilde{a}^T x \leq \tilde{b}\} (where a≠0a \neq 0, a~≠0\tilde{a} \neq 0). Also find the conditions under which the two halfspaces are equal.

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