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

11

Vote

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

5

Vote

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
4

Vote

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

1

Vote

Immanuel Bomze

http://www.tricider.com/brainstorming/xTTq