Optimizing a Constraint (mpex18)
/***************************************************************/
/* */
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: mpex18 */
/* TITLE: Optimizing a Constraint (mpex18) */
/* PRODUCT: OR */
/* SYSTEM: ALL */
/* PROCS: CLP, OPTMODEL, TRANSPOSE */
/* DATA: */
/* */
/* SUPPORT: UPDATE: */
/* REF: */
/* MISC: Example 18 from the Mathematical Programming */
/* Examples book. */
/* */
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data a_data;
input a @@;
datalines;
9 13 -14 17 13 -19 23 21
;
%let b = 37;
/* populate macro variable n as number of decision variables */
%let dsid = %sysfunc(open(a_data));
%let n = %sysfunc(attrn(&dsid, NOBS));
%let rc = %sysfunc(close(&dsid));
proc transpose data=a_data out=trans(drop=_name_) prefix=x;
run;
data condata_feas(drop=j);
length _type_ $8;
array x[&n];
set trans;
_type_ = 'le';
_rhs_ = &b;
output;
do j = 1 to &n;
x[j] = 1;
end;
_type_ = 'binary';
_rhs_ = .;
output;
run;
proc clp data=condata_feas out=out_feas allsolns usecondatavars=1;
run;
data condata_infeas;
set condata_feas;
if _N_ = 1 then do;
_type_ = 'ge';
_rhs_ = _rhs_ + 1;
end;
run;
proc clp data=condata_infeas out=out_infeas allsolns usecondatavars=1;
run;
proc optmodel;
set VARS;
set VARS0 = VARS union {0};
num a {VARS0};
read data a_data into VARS=[_N_] a;
a[0] = &b;
set FEAS_POINTS;
num x_feas {FEAS_POINTS, VARS};
read data out_feas into FEAS_POINTS=[_N_]
{j in VARS} <x_feas[_N_,j]=col('x'||j)>;
set INFEAS_POINTS;
num x_infeas {INFEAS_POINTS, VARS};
read data out_infeas into INFEAS_POINTS=[_N_]
{j in VARS} <x_infeas[_N_,j]=col('x'||j)>;
var Scale {VARS0} >= 0;
impvar Alpha {j in VARS0} = a[j] * Scale[j];
con Feas_con {point in FEAS_POINTS}:
sum {j in VARS} Alpha[j] * x_feas[point,j] <= Alpha[0];
con Infeas_con {point in INFEAS_POINTS}:
sum {j in VARS} Alpha[j] * x_infeas[point,j] >= Alpha[0] + 1;
min Objective1 = abs(a[0]) * Scale[0];
solve;
print a Scale Alpha;
min Objective2 = sum {j in VARS} abs(a[j]) * Scale[j];
solve;
print a Scale Alpha;
quit;