How to use a function like "find" during an optimization process?

[Abdullah]

Greetings,

I am using the solver IPOPT to solve a nonlinear and non-convex problem which was proposed in [1].

In a nutshell, assume we have a bounded variable t which is part of a set D. 

During the optimization process, I want the solver to find the upper and lower closest values for t from D.  Let say the solver allocates value for t = 0.14; then i want it simultaneously to find two parameters lower = 0.12 and upper = 0.22.

That has to be done during the optimization process not after termination as in some iterative methods.

Thank you.

[1] Soler, E. M., Asada, E. N., da Costa, G. R. M. (2013). Penalty-based nonlinear solver for optimal reactive power dispatch with discrete controls. IEEE Transactions on Power Systems. 28(3):2174-2182.

[Johan Löfberg]

You have to model it using binary variables and clever use of implies etc, i.e. logic programming

Your particular setup would be simple though with high-level logical ismember

x1 = sdpvar(1);
x1 = sdpvar(1);
model=[ismember(x1,[.12 .22 .32]),ismember(x2,[.12 .22 .32]),[x1<= t<=x2],abs(x1-x2)<=0.1]

[Abdullah]

Thank you Dr. Löfberg,

I tried your suggested code on a small simple example but it yields "Solver not applicable (ipopt)" error.

BTW, the proposed objective function in the literature is a penalty function to force the solver to allocate discrete values for t.

Obj = A  *  sin ( [ t / (upper-lower) ] *pi )^2

where A is a scaling factor.

[Johan Löfberg]

ipopt does not support integers hence that ismember construction won't work

that sin hack looks like a horrible hack, but what ever floats your boat...

[Abdullah]

tell me about it. 

I'm only comparing a model I'm building to this algorithm to show superiority.

In this case with the ipopt, what do you think will be the best way to do it?

[Johan Löfberg]

not using ipopt would be the only answer I can give

[Abdullah]

That defeats the purpose as the author of the paper claim they used ipopt to do this trick though GAMS!

[Johan Löfberg]

Well you can always sharpen the edge of a shovel to use it as a screwdriver, but in most cases it's probably better to simply use a screwdriver

In other words, sure use ipopt to solve mixed-integer nonlinear programs through that nonlinear penalty, but normally you are better of by using a solver developed for the purpose, or in this case by simply solving a sequence of problems instead