Matlab Newbie: How to do a simple LP with CPLEX through MATLAB

Hey guys,

I've never called CPLEX with Matlab and I was wondering how to call cplex to solve an LP?

I have the following inputs:

strings = cell(10,1) that consists of vectors of different lengths

value = cell(10,1) this holds the values of the strings

start = matrix (10,3) this is a 1 or 0 matrix if start(i) is included in string, 0 if not

end = matrix (10,3) this is a 1 or 0 matrix if end(i) is included in string, 0 if not

single = matrix (10,7) this is a 1 or 0 matrix if single(i) is included in string, 0 if not

dual = matrix (10,4) this is a 1 or 0 matrix if dual(i) is included in string, 0 if not

dualvalue = vector (1,4) this holds the values of the 'dual'

decision variable: x(s), which is binary (0,1) if string s is included, 0 if not.

obj fct: is to maximize the sum {value(s)*x(s)} + sum{dualvalue(i)*D(i)}

Constraints:

1. D(i) <= .5*(sum over all s){dual(is)*x(s)} for all i that belongs in dual

2. (sum over all s) single(is)*x(s)<=1 for all i that belongs in single

3. (sum over all s) dual(is)*x(s)<=2 for all i that belongs in dual

4. (sum over all start) x(s) - (sum over all end) x(s) = 0 for all k columns of start

5. (sum over all s) x(s) <= k

I'm using version 7.12.0; looking for the easiest way to do this; if there's an easier way by not calling cplex too, I'm all ears.

Thank you!

Andrew

[andrew]

I forgot to add, D(i) is also another decision variable, binary

Answer 1

[Titus Edelhofer]

Hi Andrew,

I don't know of a link for calling CPLEX from MATLAB (apart from using system to call CPLEX like any other program). The optimization toolbox comes with linprog to solve linear problems, allthough I must admit I did not scan through your description to look, if your problem is indeed linear ...

Titus

[andrew]

thanks, looked at linprog, but how do you solve when you have two decision variables? and also, do you have to initialize x first? ex. x = zeros( )?

[Titus Edelhofer]

No, you don't. It will be the result of the call. But I admit that I don't really see from your description, what your variables (to optimize) and what are fixed values (parameters of the optimization problem)...