# In linear optimization, what do you call a variable whose value is derived from the value of one or more decision variable?

My view of classes of variables in linear programming is as follows:

• The optimization variable (which is to be maximized/minimized)
• Decision variables (Which I control/choose the value of in order to set the variable to be optimized to ts ideal value
• External variables (Whose values are out of my control, but will determine what i should set my decision variables to, because they have an impact on the overall output of the system)
• Constraint variables (Other variables affected by the values of decision/external variables whose values must achieve minimum or maximum allowed parameters)

But what about variables whose values are derived from the values of multiple decision/external variables, but aren't constraints? i.e. let's say I'm trying to make an optimized investment, and I have a certain amount of funds to allocate to different opportunities. My decision variables are the amount of funds allocated to each investment. But what about variables such as the ratio in size of my investments to each other. I don't directly choose this value, but its value is the product of the decisions I make. Its value can potentially provide me insight about the nature of the system and future decisions. It's not a constraint, because it doesn't NEED to fall within a certain range, but what if the variable value provides me insight and understanding about the system?

I guess the problem is, if we're talking about strict mathematical optimization, then the variables I am referencing are technically unnecessary to find an optimized solution. But from a pseudo-mathematical standpoint where I am trying to understand and internalize the way a system functions and its variables interact, and manually learn how to consistently find a close to ideal solution, I find that variables like the ones I described are very useful as far as granting system understanding goes.

Do they have any kind of name? Does anyone perhaps have any insight as to how i should treat them? I guess what I'm really looking for is a proper taxonomization of these variables within my knowledge of systems I use to model/understand the world. As it stands now I don't really know what to do with them and figured maybe someone could provide additional insight.

Thanks!

• I think your use of the term "optimization variable" is nonstandard. In my mind, "optimization variable" is used synonymously with "decision variable". You might be overusing the word "variable" and should instead use the word "function" for some of these terms. For example, the objective function is the function that we are trying to maximize or minimize when we solve our optimization problem. What you are calling constraint variables I would call "constraint functions". – littleO Feb 22 '17 at 21:11
• Haha I figured I might get called out on that when I typed it. Yes, you're 100% right, it is non-standard. In my general model of understanding that I use, I tend to look at every variable as a function of other sub-variables, so at the end of the day, everything is both a variable and a function to me :p. That being said, using non-standard terminology when communicating with others wont get me far. Thanks for the input! – user1299028 Feb 22 '17 at 21:29
• These are called accounting variables and the corresponding equations: accounting rows. LP/MIP solvers are quite good in handling those as they get removed before actually solving the problem and then reintroduced at the end of the solve. – Erwin Kalvelagen Feb 23 '17 at 13:31

## 2 Answers

These are also known as defined variables (AMPL) or implicit variables (SAS).

• This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. - From Review – Klangen Jul 15 at 18:04
• I don't understand why this answer was flagged as not answering the question. The question asked what these variables are called, and I provided two names that are used. – Rob Pratt Jul 15 at 18:20
• The current state of your post qualifies it more as a comment, not an answer. If you want to "answer" a question about the definition of a variable, please provide more than a single sentence. For instance, what makes "defined" or "implicit" more adequate than "accounting" or "endogenous"? Can you provide any interesting links? Any examples? – Klangen Jul 15 at 18:37
• Added links to documentation from two commercial software vendors that use these terms. – Rob Pratt Jul 15 at 18:59
• Now it's good :) +1 – Klangen Jul 15 at 19:12

I this the term is Endogenous decision variable http://www-personal.umd.umich.edu/~delittle/Encyclopedia%20entries/Endogenous%20variable.htm