0
$\begingroup$

I have a question regarding the notion of the tangentialcone used in nonlinear optimization.

Say we have a nonconvex admissible set $X$:

$X :=\lbrace x\in\mathbb{R}^2|x_1\geq0,x_2\geq0,x_1x_2\leq0\rbrace$

The tangentialcone at $(0,0)$ is then the whole set $X$ as far as I can understand from the definition, but $X$ is not a cone?

  • 0
    No X is just the two axis' bounding the 1. quadrant – 2017-02-22
  • 0
    $X$ is a cone, just not convex... – 2017-02-22
  • 0
    But how does it fullfill the 2. property of a cone, that if you add two random elements in the cone you get a third element which is also in the cone? – 2017-02-22
  • 2
    that is a part of the definition of a **convex** cone. – 2017-02-22
  • 0
    That explains a thing or two. Thanks! – 2017-02-22

0 Answers 0