MAX SAT Optimization problem
For MAX-SAT:


The optimization problem is, given a CNF, to find the maximal number of clauses that can be satisfied at once.
The search problem is, given a CNF, to find an assignment satisfying the maximal number of clauses.
The decision problem is, given a CNF and a threshold $k$, whether there is an assignment that satisfies at least $k$ clauses.


To reduce from search to optimization, use the self-reducibility of SAT: pick a variable $x$, and try substituting $x=0$ and $x=1$, using your optimization oracle to determine which of these partial assignments leads to an assignment satisfying the maximum number of clauses.