"Lagrange multipliers"-like for inequalities (optimize algo)

[luigi]

Hi all,
it's my first post here, so: good morning!! :mrgreen: :mrgreen:

I would like to ask the following question: lagrange multipliers can be used when I have a minimization problem (like the minimum of \(\displaystyle f(x)\) ) with a constraint (like \(\displaystyle g(x)=0\) ).

What can I use when the constraint is an inequality!? for example:

minimize \(\displaystyle f(x)\) with the condition \(\displaystyle g(x)<0\)

I have found on wikipedia something named Karush-Kuhn-Tucker conditions, but I am left with beautiful theorems and no practical formulae

Any advice is appreciated, Thank you!
Luigi

 

[Deleted member 4993]

Re: "Lagrange multipliers"-like for inequalities

Hi all,
it's my first post here, so: good morning!! :mrgreen: :mrgreen:

I would like to ask the following question: lagrange multipliers can be used when I have a minimization problem (like the minimum of \(\displaystyle f(x)\) ) with a constraint (like \(\displaystyle g(x)=0\) ).

What can I use when the constraint is an inequality!? for example:

minimize \(\displaystyle f(x)\) with the condition \(\displaystyle g(x)<0\)

I have found on wikipedia something named Karush-Kuhn-Tucker conditions, but I am left with beautiful theorems and no practical formulae

Any advice is appreciated, Thank you!
Luigi

Are you doing this problem as a part of a project - or an isolated homework problem?

Anyway, what you are trying to do is called "generalized Lagrange multiplier" and is very messy (you have to deal with Jacobian of g(x) to prove existence of minima). Do a google search on "Karush-Kuhn-Tucker conditions" and you'll find several helpful (but not offering "a formula") papers to work with your given f(x) and g(x). Some of the papers work through problems - that might help.

 

[luigi]

Re: "Lagrange multipliers"-like for inequalities

Hi Subhotosh Khan,
thank you for the reply. No, this is not homework, I am just trying to optimize some algorithm for a research project :roll:

I do not want a general proof or whatever: i have simply to solve a real life problem that can be described as "minimize f(x) with g(x)<0" but I know the exact expression for f and g (or at least I am working on them :wink: )

Luigi

 

[luigi]

Re: "Lagrange multipliers"-like for inequalities

Any ideas? :mrgreen: :mrgreen:

 

[stapel]

If you're needing a research assistant, you might want to consider asking around your graduate department; a graduate may have the time and skills necessary to cooperate usefully. However, you may need to "pay" for this "help" in some manner, such as giving co-authorship to the student who write this portion of your paper for you. :idea:

FreeMathHelp is a tutoring-help forum, not a research centre. The volunteers surf by as they have time, giving help on specific homework exercises as they feel able. I'm afraid there is no paid PhD-level research staff waiting on-hand to provide guaranteed replies, do literature searches, or write papers. Sorry!

My apologies for any confusion, and my best wishes to you on your research project.

Eliz.