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  • 0 posts edited
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  • 17 votes cast
Dec
31
comment First order condition in constrained optimization: Alternative characterization via normal cones
The function $f$ is convex?
Dec
27
comment Local boundedness of monotone operators in general spaces
@NateRiver The local boundedness in the sense of equicontinuity has been completely solved recently in topological vector spaces. In simple words a monotone operator is locally bounded on the algebraic interior of its domain if and only if the space is barreled. Of course the 2nd paper you mentioned is the classical result on the topic, the third is an extension of the topic, while the first paper results on local boundedness can be found in some previous papers that are cited in that paper.
Dec
9
asked A maximal monotone operator (and not a subdifferential) with a non-convex domain
Nov
26
comment Geometric interpretation of monotone operators on a Hilbert space
@NormalHuman You're right of course. That's what I actually meant. However the ironic first sentence in your message applies probably to your friends and you could have skipped it.
Nov
24
asked Local boundedness of monotone operators in general spaces
Nov
22
comment Set of poinwise convergence of a sequence of weak* continuous linear functionals is weak* closed?
A weak star continuous linear functional on $X^*$ can be seen as an element of $X$. You need to rewrite the details of your question.
Nov
16
revised Is the algebraic interior relatively open in a closed convex set?
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Nov
16
comment Geometric interpretation of monotone operators on a Hilbert space
What you have at no. 2 is called an accretive operator in a Hilbert space.
Nov
13
comment Structure of a set whose image through continuous convex functions is an interval
Actually I reached at that formulation from a more general property applied for the level sets of a continuous convex function. It's the other problem I had a bounty for math.stackexchange.com/questions/1514768/…
Nov
13
comment Structure of a set whose image through continuous convex functions is an interval
Yes, every lsc convex function that is continuous on the interior of their domains. If it make things easier you can take all continuous convex functions defined on the whole space. Any idea would be appreciated.
Nov
13
revised Is the algebraic interior relatively open in a closed convex set?
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Nov
11
comment Relationship between affine functions and affine sets?
The graph of an affine function is an affine set.
Nov
11
revised Is the function characterized by $f(\alpha x+(1-\alpha) y) \le f^{\alpha}(x/\alpha)f^{1-\alpha}(y)$ convex?
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Nov
11
revised Is the function characterized by $f(\alpha x+(1-\alpha) y) \le f^{\alpha}(x/\alpha)f^{1-\alpha}(y)$ convex?
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Nov
11
revised Is the function characterized by $f(\alpha x+(1-\alpha) y) \le f^{\alpha}(x/\alpha)f^{1-\alpha}(y)$ convex?
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Nov
10
revised Is the function characterized by $f(\alpha x+(1-\alpha) y) \le f^{\alpha}(x/\alpha)f^{1-\alpha}(y)$ convex?
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Nov
10
revised Is the function characterized by $f(\alpha x+(1-\alpha) y) \le f^{\alpha}(x/\alpha)f^{1-\alpha}(y)$ convex?
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Nov
10
answered Is the function characterized by $f(\alpha x+(1-\alpha) y) \le f^{\alpha}(x/\alpha)f^{1-\alpha}(y)$ convex?
Nov
10
comment Is the function characterized by $f(\alpha x+(1-\alpha) y) \le f^{\alpha}(x/\alpha)f^{1-\alpha}(y)$ convex?
Actually the condition $x\ge y$ might help. Please restate the problem with all the details you wanted. Stop thanking and apologizing. It's just Math (a hobby). Read the rules of the forum.
Nov
9
revised Is the function characterized by $f(\alpha x+(1-\alpha) y) \le f^{\alpha}(x/\alpha)f^{1-\alpha}(y)$ convex?
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