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December 27th, 2014, 01:58 PM   #1
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Global optimality of a convex but non-smooth function

I have a question. The answer may be too obvious but I cannot be sure about the right answer. Let say that we have a convex but non-smooth function which is defined as f:R2→R. For a point in R2, if we know that the function increases for the directions (1,0), (−1,0), (0,1) and (0,−1), can we sure about that this point is local optimum (because of the convexity it will be also global optimum)?

Thank you in advance.
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convex, convex optimization, function, global, global optimality, nonsmooth, nonsmooth function, optimality



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