It depends on how you interpret omnipotence and the ability of God.
/puts on philosophical history cap/
If you take the view of Descartes, then God's omnipotence could possibly mean that he could do things that are logically impossible, because logic is a construct of human existence, and not necessarily a construct of divine existence. In other words, someone like Descartes would argue that God is absolutely powerful, and therefore could create a rock that is too heavy for him to lift, and then lift it. There is a problem from our perspective, but from God's perspective there is no problem, and it is entirely feasible.
If you take the view of someone like Thomas Aquinas, it's nonsensical for God to be able to do something logically impossible, but then it is logically impossible for God to do something like make a stone he cannot lift. The reason he cannot do so is not that he lacks the ability to make said stone, but because it is simply a logically empty statement. The idea that an infinitely powerful could create something more powerful than infinite power is a meaningless and incoherent statement, and thus falls outside the bounds of possible activity, description or logic.
Under either view, the stone problem is not actually a problem.
As a side note, if you follow along with someone like Augustine, then the real basis of God's power is not so much to do with logic, but with will. In other words, what makes God all powerful is not whether he can do this thing or that thing, but rather the idea that whatever God wills, happens. The advantage of this view theologically is that it actually finds quite a lot of scriptural foundation. Thus, applying this view to the rock problem, one would have to question why God would want to make an all powerful rock in the first place, and then that would determine whether he would/could.
/removes hat