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700 days left

What notation should be used for the copositive and completely positive cones?

Dear respected colleague,

The aim of this poll is to attempt to reach a consensus on the notation to use for the copositive and completely positive cones.

When taking part in this vote, PLEASE VOTE WITH YOUR FULL NAME. This is to try to prevent double voting. I have included a few ideas for notation, along with some of their pros and cons. Please feel free to add to these. Also, please invite and encourage other people you know from the field to take part in this vote. An alternative url for sharing this vote is: http://tinyurl.com/copositivenotation.

Thank you in advance for taking the time to vote.

Regards,
Peter J.C. Dickinson
University of Twente


saved
Ideas
Pros and cons
 
Votes
Copositive = \mathcal{COP}; Completely positive = \mathcal{CP}
by Peter J.C. Dickinson
 
The other two alternatives would mean many people in the field swapping to the exact opposite not... more
by Peter J.C. Dickinson
1
 
This notation suggests that the cones being mutually dual is one of their properties, rather than... more
by Peter J.C. Dickinson
1
 
Maybe with a lowercase o in CoP.
by Imre Polik
1
 
Adding to the first pro argument: This seems the better option for a talk when the audience is no... more
by Naomi Shaked-Monderer
 
C is used for a cycle. CP says that we talk about cp matrices. CP COP (or C0P) is more symmetrical
3
 
Using \mathcal{CP} agrees well with the well established notion of the cp-rank
by Mirjam Duer
 
Although I stated my preference for another option previously, this option for CP and COP has gro... more
by Sam Burer
Add argument
 
11

Leslie Hogben, Zhichao Zheng, and 8 more

Copositive = \mathcal{C}; Completely positive = \mathcal{C}^\ast
by Peter J.C. Dickinson
 
The subject is called copositive programming/optimisation, so the primal cone should be the copos... more
by Peter J.C. Dickinson
1
 
The definition of copositivity extends more naturally to infinite dimensions than complete positi... more
by Peter J.C. Dickinson
 
Taking a quick sample of papers on copositivity by searching "copositive" on google scholar, I fi... more
by Peter J.C. Dickinson
 
C by itself is not descriptive enough, and it is used as a general letter to denote cones or conv... more
by Imre Polik
 
Agree with Imre's comment
by Kurt Anstreicher
Add argument
5

Bolor Jargalsaikhan, Roland Hildebrand, Mirjam Duer and 2 more

Copositive = \mathcal{C}^\ast; Completely Positive = \mathcal{C}
by Peter J.C. Dickinson
 
In the well known 2009 paper by Burer, a large class of problems was given a formulation as a con... more
by Peter J.C. Dickinson
 
Even though the 2009 paper by Burer looks at a completely positive formulation, it still uses the... more
by Peter J.C. Dickinson
1
 
"Completely positive" has many different meanings in mathematics, so to avoid confusion the subje... more
by Peter J.C. Dickinson
 
I was told (but I have not understood the whole argument) that the infinite-dimensional completel... more
by Sam Burer
 
In every copositive representation I am aware of (not just my 2009 paper), the completely positiv... more
by Sam Burer
 
Primal containing original variables makes a lot of sense to me.
by Hongbo Dong
1
Add argument
4

Karthik Natarajan, Adam Letchford, Hongbo Dong and 1 more

I like Imre's idea of CoP for copositive; I dislike unbalanced lengths for both cones, so I prefer CpP for completely positive
by Immanuel Bomze
 
does not work, since \mathcal does not allow lower case letters
Add argument
1
Immanuel Bomze

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