Math Is Fun Forum

schreiber

Guest

what means "binding in equilibrium" ?

hi there,
im a german student and ive come across a phrase that is:
(2) and (5) are binding in equilibrium, and (3) and (4) are slack.

2,3,4,5 are given equations, but
can anyone explain that to me, so i can, without any knowloedge of the special mathematic vocabulary in english, translate it myself?
i know what an equilibrium is, but the rest i dont, specially not the context.

PLEASE help!
THX

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: what means "binding in equilibrium" ?

Hi schreiber;

Are you doing a linear optimization problem because they use slack variables?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

schreiber

Guest

Re: what means "binding in equilibrium" ?

see thats the point. i have no idea what this is about. what does slack even mean? is there no other way to describe it?
thank you

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: what means "binding in equilibrium" ?

In an optimization problem a slack variable is used to turn an inequality into an equation.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

schreiber

Guest

Re: what means "binding in equilibrium" ?

well, i do not understand.
what about the term "binding in equilibrium"? what does that mean?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: what means "binding in equilibrium" ?

Hi schreiber;

That I don't know. Unless you can give me a little more, I am unable to help.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

schreiber

Guest

Re: what means "binding in equilibrium" ?

its all in this paper. link is: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=286165

my problem is on page 15/33: lemma 1.

thank you, bobby!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: what means "binding in equilibrium" ?

OK. I am there but I can't find page 15/33

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

schreiber

Guest

Re: what means "binding in equilibrium" ?

the pdf file that u get has 33 pages. did u click on the download button on top?
thx

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: what means "binding in equilibrium" ?

Yep, says that is not a downloadable file. I am on a Social science reseatch network. Is that correct?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

schreiber

Guest

Re: what means "binding in equilibrium" ?

hm, i just downloaded it there. from the server in NYC. it has to work.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: what means "binding in equilibrium" ?

Hi schreiber;

  Yes, it a optimization problem where as near as I can tell they are maximizing p usually means profit, the others are slack variables. The rest I can not understand, something about a provider they are using.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

schreiber

Guest

Re: what means "binding in equilibrium" ?

1st of all, thank you for looking into this.
well, the context is totally clear to me, the thing about the provider and so on.
they try to maximize, i think, the "Se,Si" whats written underneath the word "max". the p stands for probability like: p[...]+(1-p)[...]

now my questions are:
1) what does the words "slack" and "binding in equilibrium" in a mathematical sense mean?
2) why are equations 2 and 5 in the paper binding and why are 3 and 4 slack(whatever it means)?

can u help me with that?
THX!!!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: what means "binding in equilibrium" ?

Hi schreiber;

1)  The slack variables are variables that are added to constraints to turn inequalities into equations. For instance If z > x+y then I can say z = x+y+c where c is some unknown constant. c is a slack variable. I don't understand the binding in equilibrium in any sense, I suspect it is particular to their problem.

2)  Unfortunately I am unable to follow the reasoning for ( 2,5,3,4). That is all I can say concerning this problem, I am sorry I could not be of more help,

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

schreiber

Guest

Re: what means "binding in equilibrium" ?

alright,
thank you for your help anyway!
hope i can use what u said about the slack thing, at least its clearer than before to me.
thx, i really appreciate!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: what means "binding in equilibrium" ?

Just hope it helped a little.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.