I am an electrical engineer who is currently working with some optimization problem. One of my senior has a strange rule of thumb to determine the convexity of constraint for minimization problem.
His rules for this constraint are listed as follows:
$f\left( x \right) \le g\left( x \right)$
1/ If $f\left( x \right)$ is a convex function and $g\left( x \right)$ is a linear function then the constraint $f\left( x \right) \le g\left( x \right)$ can be written as a convex constraint.
2/ If $f\left( x \right)$ is a convex function and $g\left( x \right)$ is a concave function then the constraint $f\left( x \right) \le g\left( x \right)$ can be written as a convex constraint.
The problem is that most people in my group just follow this without asking any question. Therefore, I was wondering if this is true or not since there is no proof.
Would you kindly help me with this ?
Thank you for your enthusiasm !