## Linear Least-Squares Problem (qpsol1)

```
/***************************************************************/
/*                                                             */
/*          S A S   S A M P L E   L I B R A R Y                */
/*                                                             */
/*    NAME: qpsol1                                             */
/*   TITLE: Linear Least-Squares Problem (qpsol1)              */
/* PRODUCT: OR                                                 */
/*  SYSTEM: ALL                                                */
/*    KEYS: OR                                                 */
/*   PROCS: OPTMODEL                                           */
/*    DATA:                                                    */
/*                                                             */
/* SUPPORT:                             UPDATE:                */
/*     REF:                                                    */
/*    MISC: Example 1 from the Quadratic Programming Solver    */
/*          chapter of Mathematical Programming.               */
/*                                                             */
/***************************************************************/

/* example 1: linear least-squares problem */
proc optmodel;
var x1; /* declare free (no explicit bounds) variable x1 */
var x2; /* declare free (no explicit bounds) variable x2 */
/* declare slack variable for ranged constraint */
var w >= 0 <= 0.2;

/* objective function: minimize is the sum of squares */
minimize f = 26 * x1 * x1 + 5 * x2 * x2 + 10 * x1 * x2
- 14 * x1 - 4 * x2 + 2;

/* subject to the following constraint */
con L: 3 * x1 + 2 * x2 - w = 0.9;

solve with qp;

/* print the optimal solution */
print x1 x2;
quit;

```