Thank you very much, I like this solution! Looking forward testing it ... View more

It's working perfectly, thank you! ... View more

Glad to help! ... View more

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! ... View more

Glad to help 🙂 Can't test it right not, but it looks right to me. ... View more

Will use Enterprise Guide then, as long as it does the job I'm fine with that. Thank you again! ... View more

Just received my new licence and this is 9.4TS1M5 with SAS/OR 14.3... I guess I will discover the 15.1 when you'll be at version 16 or higher ... View more

Here's another approach that might be simpler to digest. %let n = 4; data MVC_sparse(keep=grp name name2 cov); set MVC; array covarray [&n] _1-_&n; do j = 1 to &n; Name2 = '_'||put(j,1.); cov = covarray[j]; if cov ne . then output; end; run; %let byvar = grp; /* BY group processing */ proc optmodel; /* Declare the sets of parameters and data indexed by sets */ set OBS; num grp {OBS}; str asset_i {OBS}; str asset_j {OBS}; number MVC{OBS}; /* Populate the model by reading in the specific data instance */ read data Work.MVC_sparse into OBS=[_N_] grp asset_i=Name asset_j=Name2 MVC=cov; set ASSETS = setof {o in OBS} asset_i[o]; /* Collect values of BY variable into an index set */ set BYSET = setof {i in OBS} &byvar.[i]; num by; /* Declare the variable */ set OBS_BY = {i in OBS: &byvar.[i] = by}; set Assets_BY = setof {o in OBS_BY} asset_i[o]; var W{Assets_BY} >= 0; /* Minimize the objective function (variance of the portfolio) */ minimize Variance = sum{o in OBS_BY}W[asset_i[o]]*MVC[o]*W[asset_j[o]]; /* Subject to the following constraints */ con BUDGET: sum{i in Assets_BY}W[i] = 1; /* Declare parameters to store solution values */ num W_sol {BYSET, ASSETS}; /* Loop over values of the BY variable, calling the QP solver once for each level. Note that OBS_BY is automatically updated when the BY variable changes. */ /* do by = BYSET;*/ cofor {b in BYSET} do; by = b; put by=; solve; /* Store solution in numeric parameters */ for {i in Assets_BY} W_sol[by,i] = W[i].sol; end; /* Save the solutions for all values of the BY variable simultaneously */ create data weights_sparse(where=(W ne .)) from [&byvar i] W=W_sol; quit; ... View more

For more about generalized inverses and solving the rank-deficient regression problem, see the articles "Generalized inverses for matrices" and "Singular parameterizations, generalized inverses, and regression estimates"   ... View more

Oh! I did it the hard way, because I didn't know that BTRAN existed.  Perhaps you should blog about it Rick, to try and get it more widely known? ... View more

Thank you so much Rick! I was indeed missing the point that the mean has to be weighted too. ... View more

Blog post on implementing fixed-bandwidth kernel regression in SAS/IML. ... View more

Or use SYMGET() and you don't need care about if it is numeric or character.   proc sql noprint; select distinct age into : list separated by ',' from sashelp.class; quit; data want; set sashelp.class; if findw(symget('list'),strip(age),','); run; proc sql noprint; select distinct name into : list separated by ',' from sashelp.class; quit; data want; set sashelp.class; if findw(symget('list'),strip(name),','); run; ... View more