Are unions, sums (…) of quasiconvex functions again quasiconvex?
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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
convex-analysis
asked Apr 27 '15 at 5:46
BrittaNBrittaN
11
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add a comment |
$begingroup$
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
convex-analysis
asked Apr 27 '15 at 5:46
BrittaNBrittaN
11
$endgroup$
add a comment |
$begingroup$
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
convex-analysis
asked Apr 27 '15 at 5:46
BrittaNBrittaN
11
$endgroup$
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
convex-analysis
convex-analysis
asked Apr 27 '15 at 5:46
BrittaNBrittaN
11
asked Apr 27 '15 at 5:46
BrittaNBrittaN
11
asked Apr 27 '15 at 5:46
BrittaNBrittaN
11
asked Apr 27 '15 at 5:46
BrittaNBrittaN
11
asked Apr 27 '15 at 5:46
BrittaNBrittaN
11
11
add a comment |
add a comment |
1 Answer
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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?
answered Apr 27 '15 at 6:40
Mehdi Jafarnia JahromiMehdi Jafarnia Jahromi
1,164615
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$begingroup$
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!
$endgroup$
– BrittaN
Apr 27 '15 at 6:43
add a comment |
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1 Answer
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1 Answer
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$begingroup$
Sum of two quasiconvex functions need not to be quasiconvex. Have you seen this http://en.wikipedia.org/wiki/Quasiconvex_function?
answered Apr 27 '15 at 6:40
Mehdi Jafarnia JahromiMehdi Jafarnia Jahromi
1,164615
$endgroup$
$begingroup$
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!
$endgroup$
– BrittaN
Apr 27 '15 at 6:43
add a comment |
$begingroup$
Sum of two quasiconvex functions need not to be quasiconvex. Have you seen this http://en.wikipedia.org/wiki/Quasiconvex_function?
answered Apr 27 '15 at 6:40
Mehdi Jafarnia JahromiMehdi Jafarnia Jahromi
1,164615
$endgroup$
$begingroup$
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!
$endgroup$
– BrittaN
Apr 27 '15 at 6:43
add a comment |
$begingroup$
Sum of two quasiconvex functions need not to be quasiconvex. Have you seen this http://en.wikipedia.org/wiki/Quasiconvex_function?
answered Apr 27 '15 at 6:40
Mehdi Jafarnia JahromiMehdi Jafarnia Jahromi
1,164615
$endgroup$
Sum of two quasiconvex functions need not to be quasiconvex. Have you seen this http://en.wikipedia.org/wiki/Quasiconvex_function?
answered Apr 27 '15 at 6:40
Mehdi Jafarnia JahromiMehdi Jafarnia Jahromi
1,164615
answered Apr 27 '15 at 6:40
Mehdi Jafarnia JahromiMehdi Jafarnia Jahromi
1,164615
answered Apr 27 '15 at 6:40
Mehdi Jafarnia JahromiMehdi Jafarnia Jahromi
1,164615
answered Apr 27 '15 at 6:40
Mehdi Jafarnia JahromiMehdi Jafarnia Jahromi
1,164615
1,164615
$begingroup$
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!
$endgroup$
– BrittaN
Apr 27 '15 at 6:43
add a comment |
$begingroup$
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!
$endgroup$
– BrittaN
Apr 27 '15 at 6:43
$begingroup$
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!
$endgroup$
– BrittaN
Apr 27 '15 at 6:43
$begingroup$
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!
$endgroup$
– BrittaN
Apr 27 '15 at 6:43
add a comment |
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