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Jan 16, 2011 at 22:11 history edited Rajhans CC BY-SA 2.5
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Jan 15, 2011 at 22:24 comment added Igor Rivin There is a large literature on maximizing differences of two convex functions, as you can see by googling: "maximizing difference of two convex functions" Much of this literature addresses bounds of the sort you are interested in.
Jan 15, 2011 at 22:14 history asked Rajhans CC BY-SA 2.5