Mixing
Quasiconvexity + X implies convexity
0
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Given a continuous function $f$ that is quasi-convex over some interval $[a,b] subset mathbb{R}$, what are examples of additional (sets of) properties (themselves weaker than convexity) that ensure that $f$ is also convex over that interval?
convex-analysis convex-optimization convex-geometry
asked Feb 3 at 12:48
PaulPaul
134
$endgroup$
add a comment |
0
$begingroup$
Given a continuous function $f$ that is quasi-convex over some interval $[a,b] subset mathbb{R}$, what are examples of additional (sets of) properties (themselves weaker than convexity) that ensure that $f$ is also convex over that interval?
convex-analysis convex-optimization convex-geometry
asked Feb 3 at 12:48
PaulPaul
134
$endgroup$
1
$begingroup$
Quasi-convexity is a pretty weak starting point. How are you going to use what quasi-convexity gives you (convex level sets) together with other features to get to convexity?
$endgroup$
– Brian Borchers
Feb 3 at 20:30
2
$begingroup$
I doubt there's any particularly interesting answer here. I'll bet any additional condition people think of will get you convexity by itself.
$endgroup$
– Michael Grant
Feb 3 at 21:03
add a comment |
0
0
0
$begingroup$
Given a continuous function $f$ that is quasi-convex over some interval $[a,b] subset mathbb{R}$, what are examples of additional (sets of) properties (themselves weaker than convexity) that ensure that $f$ is also convex over that interval?
convex-analysis convex-optimization convex-geometry
asked Feb 3 at 12:48
PaulPaul
134
$endgroup$
Given a continuous function $f$ that is quasi-convex over some interval $[a,b] subset mathbb{R}$, what are examples of additional (sets of) properties (themselves weaker than convexity) that ensure that $f$ is also convex over that interval?
convex-analysis convex-optimization convex-geometry
convex-analysis convex-optimization convex-geometry
asked Feb 3 at 12:48
PaulPaul
134
asked Feb 3 at 12:48
PaulPaul
134
asked Feb 3 at 12:48
PaulPaul
134
asked Feb 3 at 12:48
PaulPaul
134
asked Feb 3 at 12:48
PaulPaul
134
134
1
$begingroup$
Quasi-convexity is a pretty weak starting point. How are you going to use what quasi-convexity gives you (convex level sets) together with other features to get to convexity?
$endgroup$
– Brian Borchers
Feb 3 at 20:30
2
$begingroup$
I doubt there's any particularly interesting answer here. I'll bet any additional condition people think of will get you convexity by itself.
$endgroup$
– Michael Grant
Feb 3 at 21:03
add a comment |
1
$begingroup$
Quasi-convexity is a pretty weak starting point. How are you going to use what quasi-convexity gives you (convex level sets) together with other features to get to convexity?
$endgroup$
– Brian Borchers
Feb 3 at 20:30
2
$begingroup$
I doubt there's any particularly interesting answer here. I'll bet any additional condition people think of will get you convexity by itself.
$endgroup$
– Michael Grant
Feb 3 at 21:03
1
1
$begingroup$
Quasi-convexity is a pretty weak starting point. How are you going to use what quasi-convexity gives you (convex level sets) together with other features to get to convexity?
$endgroup$
– Brian Borchers
Feb 3 at 20:30
$begingroup$
Quasi-convexity is a pretty weak starting point. How are you going to use what quasi-convexity gives you (convex level sets) together with other features to get to convexity?
$endgroup$
– Brian Borchers
Feb 3 at 20:30
2
2
$begingroup$
I doubt there's any particularly interesting answer here. I'll bet any additional condition people think of will get you convexity by itself.
$endgroup$
– Michael Grant
Feb 3 at 21:03
$begingroup$
I doubt there's any particularly interesting answer here. I'll bet any additional condition people think of will get you convexity by itself.
$endgroup$
– Michael Grant
Feb 3 at 21:03
add a comment |
0
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1
$begingroup$
Quasi-convexity is a pretty weak starting point. How are you going to use what quasi-convexity gives you (convex level sets) together with other features to get to convexity?
$endgroup$
– Brian Borchers
Feb 3 at 20:30
2
$begingroup$
I doubt there's any particularly interesting answer here. I'll bet any additional condition people think of will get you convexity by itself.
$endgroup$
– Michael Grant
Feb 3 at 21:03