How can you show that $f(x_1,x_2) = (x_1 – x_2)^4 – 5 x_1 x_2$ is not coercive?
I somehow have to show that $\lim_{||x||\to\infty} \neq \infty$.
I tried expressing the function as a function of $x_1^2+x_2^2$, but I couldn't find an expression for which I could deduce the limit. Can someone tell me how to do this?
Show $f(x_1,x_2) = (x_1-x_2)^4 – 5 x_1 x_2$ is not coercive
coercivenonlinear optimizationoptimization
Best Answer
Since $\underset{x_1 \to \infty}{\lim} f(x_1,x_1) = \underset{x_1 \to \infty}{\lim} -5x^2_1 = -\infty$, we have $\underset{\lVert x \rVert \to \infty}{\lim} f(x_1,x_2) \neq \infty$.