Questions tagged [local-minimum]
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2
questions
3
votes
1answer
79 views
Radial unboundedness vs convexity
We have a simple problem, namely minimizing:
$$f(x) = x_1^2 + x_2^2 - x_1.$$
The gradient is $$\nabla f(x) = \begin{bmatrix} 2x_1 - 1 \\ 2x_2 \end{bmatrix},$$
hence the unique stationary point is: $...
5
votes
1answer
383 views
Single KKT solution for a simple problem: proof of being minimizer
I have a very simple problem:
$$ \begin{align*}
\begin{array}{ll}
\min\limits_{x_1,x_2} & -x_1x_2 \\
\text{s.t.} & x_1 + x_2 - 2 = 0.
\end{array}
\end{align*} $$
The KKT system gives me $x_1^*...
