"or" constraints and lagrange multipliers

[djami]

Hello,

I have a resource allocation problem where I would like to maximise a function subject to the constraint that each allocation xi is either 0 or >= ci, for some ci>0. I am having trouble finding any examples or references to these kinds of constraints. Does anyone know if they have a particular name and/or can anyone provide any references to books or papers that discuss such constraints?

Thanks,

 

[Ishuda]

Hello,

I have a resource allocation problem where I would like to maximise a function subject to the constraint that each allocation xi is either 0 or >= ci, for some ci>0. I am having trouble finding any examples or references to these kinds of constraints. Does anyone know if they have a particular name and/or can anyone provide any references to books or papers that discuss such constraints?

Thanks,

The general class of problems is called Mathematical Programming, if the function you want to maximize is linear, Linear Programming. Google should gives some more information.

BTW: If your function is not linear and especially if you plan to continue in this as a career, I suggest you might take a look at Numerical Methods That Usually Work by Forman S. Acton which I first read almost 50 years ago [actually the updated version, Numerical Methods That Work would probably be better].

 

[djami]

The general class of problems is called Mathematical Programming, if the function you want to maximize is linear, Linear Programming. Google should gives some more information.

BTW: If your function is not linear and especially if you plan to continue in this as a career, I suggest you might take a look at Numerical Methods That Usually Work by Forman S. Acton which I first read almost 50 years ago [actually the updated version, Numerical Methods That Work would probably be better].

Hi Ishuda,

Thanks for your reply. What I was looking for was the name of "semi- continuous" variables which I have since found. I knew about mathematical programming but seemed to only find references to constrained or bounded variables and couldn't work out what variables with a disjoint domain ({0} U [a,b]) were called.

The book you recommended sounds very useful, I'll check it out!

Cheers,
Djami