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for a project I need to prove quasiconvexity of several general functions. Can I argue that the union (or sum, or difference...) of quasiconvex functions is again quasiconvex? I do know that the sum of convex functions is again convex, does this apply to quasiconvexity?

My functions may include the log-function, which is quasiconvex but not convex (for example).

Thank you very much for your help.

Best wishes, Britta

BrittaN
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1 Answers1

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Sum of two quasiconvex functions need not to be quasiconvex. Have you seen this http://en.wikipedia.org/wiki/Quasiconvex_function?

Mehdi Jafarnia Jahromi
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  • Thank you very much.

    I did see that, however, it does not answer my question for any other union of functions

    i.e. log(x^2+b) or something like that.

    Thanks a lot!

     – BrittaN Apr 27 '15 at 06:43