Thank you for the comments and answers!
Show if the function is coercive:
$$f(x,y) = x^2 + y^2 – xy – x$$
Have some difficulties dealing with the last $x$ term, tried to replace it with $|xy|$, didn't work. Could someone give me some hints of how to approach such question.
Note: definition of coercive, $$f(z)\rightarrow +\infty, as \ \|z\|\to\infty $$
Best Answer
Hint: $f(z)=z^THz+c^Tz$ with invertible $H$ can be written as $$ f(z)=(z+\frac12H^{-1}c)^TH(\underbrace{z+\frac12H^{-1}c}_{\hat z})-\frac14c^TH^{-1}c=g(\hat z). $$ Now $f$ is coercive iff $g$ is coercive.