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The topic of the material is convex optimization. The relevant textbook is Convex Optimization, Boyd &...

The topic of the material is convex optimization. The relevant textbook is Convex Optimization, Boyd & Vandenberghe.

Problem 1. Let K be a subset of some finite-dimensional real vector space,
and assume that:

For all x in K, all alpha greater than 0 : alpha x in in K.
In other words, assume that K is a cone in V . Show that
K is a convex set if and only if for all x, y in K: x + y is in K.

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