The best way to write a large number of constraints for an optimization problem

Hi All,

I have an optimization problem which have a larger number of variables, probably 10000 optimization variables and a large number of constraints. The optimization problem is mixed integer convex problem. What is the best way to define the large number of constraints?. Can I use loops like the ones used in CVX to define constraints?. I have matlab 2013a.

Thank you

Answer 1

[Matt J]

If they are linear constraints, they will be expressed using matrix-vector multiplication

A*x<=b
Aeq*x<=beq

so any vectorized method for building the A, Aeq, b, beq, matrices would be appropriate. Similarly, nonlinear constraints in Matlab are expressed using user-defined constraint functions of the following form

function [cineq,ceq]=nonlcon(x)

  ....

end

where cineq and ceq are vectors of inequality and equality constraint violations, respectively. When the number of variables or constraints is large, you would use vectorized Matlab commands to generate cineq and ceq from x.

[mohamed Faraj]

My optimization variable is written as x= [x(1) x(2)...x(468)]. The objective function is fun=x(1)+x(2)+.....x(24). The variable from x(2) to x(468) are all zeros in the objective function. How can I do this in matlab?.

[Matt J]

fun=@(x) sum(x(1:24));

[mohamed Faraj]

Thank you Matt. For the nonlinear constraints. My optimization vector is x which is x=[x(1) x(2)...x(408)]. I have many constraints but for test purposes, I tried one constraint which has a subset of the variables

function [c,ceq]=nonlcon(x)
c=1/(x(1)-sum(x(25:40)))+1/x(73)+1/x(169)-5;
ceq=[];

When I run the code, it gives an error that not enough input arguments in the line fmincon.

[Matt J]

When I run the code

Code you haven't shown, so it's anybody's guess what's wrong with it....

However, my guess would be that your call to fmincon looks like this

fmincon(_____,nonlcon)

instead of this

fmincon(_____,@nonlcon)

[mohamed Faraj]

It works now with @. Thank you.