Linear Least-Squares Problem (qpsol1)
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/* */
/* 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. */
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/* 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;