About optimization tool box question

How can I do so that the summation in the constraint can be applied in the fmincon function which used in optimization tool box?

Plz, help and thanks a lot!!

[Ho Chun]

Thanks for all your help!!

Re: Johan Löfberg

Does the CVX mean convex optimization? If I use that tool, is there any suggestion where I can get the tool cuz I only get Matlab. BTW, how can I apply the constraint in CVX? For example, how to apply the summation in the CVX. Thanks for your help!

Answer 1

[Alan Weiss]

I am not sure that I understand the difference between p_i and p_i^h. But the constraints look like bounds and linear equality constraints.

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[John D'Errico]

What confuses me is that if p_i is in the interval [0,1] then usually p_i^h (assuming that is a power we are talking about) is also in that interval. So those bound constraints all reduce to the simple

0 <= p_i <= 1

Again, this assumes that p_i^h is p_i raised to the power h. I suppose that superscript might be defined in any way you like, but if you want us to understand mathematics, then you need to either let us assume that your notation is consistent with standard mathematical notation, or tell us how it is not.

Next, the first equality constraint does not seem to be linear, since it also has powers of the p_i in the sum.

Finally, we don't know what values M and H take on, but there are apparently M unknowns to search over, but we see M+H equality constraints. And that ignores the bound constraints. This is a recipe for a situation with no possible solutions that satisfy the equality constraints.

Answer 3

[Johan Löfberg]

Looks like a QP to me (i.e., you should not use fmincon, but quadprog, or some other quadratic programming solver)

You have two sets of variables, the vector p, and a matrix P (the one you index with i and h). You have bound constraints on all elements in P, the equality p = P*q and sum of rows equals 1, sum(P,1)=1. To get this into a numerical format for quadprog, you have to introduce a vectorized notation where your decision variables are x =[p;P(:)], and then simply write all constraints in terms of this vector.

Alternatively, you can use a MATLAB based modelling layer such as YALMIP or CVX. Here is the YALMIP code to solve the problem

p = sdpvar(M,1);
P = sdpvar(M,H,'full');
Constraints = [p == P*q, 0 <= P <= 1, sum(P,1) == 1];
Objective = p'*p;
optimize(Constraints,Objective)
value(p)
value(P)

[Ho Chun]

Re: Johan Löfberg

Does the CVX mean convex optimization? If I use that tool, is there any suggestion where I can get the tool cuz I only get Matlab. BTW, how can I apply the constraint in CVX? For example, how to apply the summation in the CVX. Thanks for your help!

[Johan Löfberg]

CVX and YALMIP are two different MATLAB toolboxes for convex optimization (and many other problem classes in the case of YALMIP). The code above is YALMIP code, and you can download the toolbox from http://users.isy.liu.se/johanl/yalmip/

[Ho Chun]

But I have to minimize the objective, is it minimize by typing optimize(...)? Thank you.

[Johan Löfberg]

Precisely as the code I gave. To minimize Objective subject to Constraints, you do optimize(Constraints,Objective)

Please study the YALMIP Wiki with all the examples and tutorials

[Karthikeyan Nainar]

The equality sum(P,1)=1 looks like sum of columns and not rows.

Answer 4

[Ho Chun]

Thanks for all your help!!

Re: Johan Löfberg

Does the CVX mean convex optimization? If I use that tool, is there any suggestion where I can get the tool cuz I only get Matlab. BTW, how can I apply the constraint in CVX? For example, how to apply the summation in the CVX. Thanks for your help!

Answer 5

[Ho Chun]

BTW, M is a user input value, which can be 3 or 5. H can be 20.