Does the Omni God Limit Himself?

Recently, while reading a blog post by Roger Olson I came across the following—from him—in response to one of the comments.

[The Bible] suggests that our praying can make a real difference in how God acts for the good. I can only speculate that is due to some self-limitation of God for the sake of our participation in his mission to the world. (emphasis mine)

Does the all knowing, all powerful, omni God place self-imposed limits upon His knowledge, power, will, etc.? Some would think such a question to be foolish and could not conceive of God doing such a thing. Be that as it may, there are some passages in the Scriptures that do support the idea.

For instance, Isaiah 43:25,  Hebrews 8:12 and 10:17  each remind us that the all knowing God—on the basis of His forgiveness—no longer remembers our sins. In interpreting such passages we will often employ wording like, “God chooses not to remember our sins.” I certainly agree that this is true, but it does infer that God chooses to limit His omniscience. 2 Peter 3:9 tells us that God is not willing that any should perish, yet we know that many do in fact perish. Apparently the all powerful God also limits His power.

This then begs the question, “In what other ways does God limit Himself?”