Converting maximization to minimization in aproximation algorithms Suppose algorithm A is given for a maximization problem and we are asked to show that it is a 1/2-approximation algorithm. 

As you know it is enough to show

Sol >= 1/2 OPT

What I need to know is, is it true to assume this problem as a minimization one and prove

Sol &lt;= 2 OPT

Or is there any correspondence between these two?
One connection is that maximizing some function $f$ is the same as minimizing its reciprocal $1/f$. You can use this to convert between maximization and minimization.

The general problem of maximizing a function $f$ under some constraints can be very different from the corresponding minimization problem (of the same function $f$). A case in point is MIN-CUT versus MAX-CUT. Whereas MIN-CUT is in P, MAX-CUT is NP-hard to approximate better than some constant.