proc optmodel / Results not sastifying constraints

[Alain38]

Hello,

I wrote the following code that determines the weights maximizing a ratio. These weights should be positive given the constraint on variables:

	var W{Assets_BY} >= 0 <= 0.1;

but many of them are actually negative (admittedly small, with order E-7). However, when I rescale them so that their sum is equal to 1, they are no longer negligible with the smaller value being equal to -0.135.

%let byvar = grp;
proc optmodel printlevel=0;
	set OBS;
	num grp {OBS};
	set <string> Assets;
	set <num,str> GROUPS_ASSETS;
	number MVC{GROUPS_ASSETS, Assets};

	read data Work.MVC into Assets=[Name];
	read data Work.MVC into OBS=[_N_] grp;
	read data Work.MVC nomiss into GROUPS_ASSETS=[k=grp i=Name] {j in Assets} <MVC[k,i,j]=col(j)>;

	set BYSET = setof {i in OBS} &byvar.[i];
	num by;

	set OBS_BY = {i in OBS: &byvar.[i] = by};
	set Assets_BY = setof {o in OBS_BY, <(grp[o]),a> in GROUPS_ASSETS} a;
	var W{Assets_BY} >= 0 <= 0.1;
	impvar Denom = sqrt(sum{i in Assets_BY, j in Assets_BY}W[i]*MVC[by,i,j]*W[j]);

	maximize DR =  log(sum{i in Assets_BY}W[i]*sqrt(MVC[by,i,i]) / Denom);

	num W_sol {GROUPS_ASSETS};
	do by = BYSET;
		put by=;
		solve;
		for {i in Assets_BY} W_sol[by,i] = W[i].sol;
	end;

	create data Work.Weights_MD from [&byvar i] W=W_sol;
quit;

Thank you for any advice to obtain weights that respect the lower and upper bounds,

Best,

PS: if necessary, I will provide a small working example

[RobPratt · Accepted solution]

The default feasibility tolerance is 1e-6, so 1e-7 is within that tolerance.  You can change the value by using the FEASTOL= option.

If you want the sum of W to be 1, it might be best to explicitly declare such a constraint.  If that doesn't suffice, please share your data.

[Alain38]

Thank you very much for your help 🙂

I will try to define a lower feasibility tolerance. As for the "sum of weight" constraint, I removed it because it was much longer with it, but perhaps it will be more efficient than a lower feasibility tolerance. I will perform some tests. Thank you!