Solving Large-Scale NLP Problems (nlpse05)

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/*               S A S   S A M P L E   L I B R A R Y             */
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/*     NAME: nlpse05                                             */
/*   TITLE: Solving Large-Scale NLP Problems (nlpse05)           */
/* PRODUCT: OR                                                   */
/*  SYSTEM: ALL                                                  */
/*    KEYS: OR                                                   */
/*   PROCS: OPTMODEL                                             */
/*    DATA:                                                      */
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/* SUPPORT:                             UPDATE:                  */
/*     REF:                                                      */
/*    MISC: Example 5 from the Nonlinear Programming Solver      */
/*          chapter of Mathematical Programming.                 */
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proc optmodel;
   num nx = 100;
   num ny = 100;

   var x {1..nx, 0..ny+1} >= 0;
   var y {0..nx+1, 1..ny} >= 0;

   min f = (
        sum {i in 1..nx-1, j in 1..ny-1} (x[i,j] - 1)^2
      + sum {i in 1..nx-1, j in 1..ny-1} (y[i,j] - 1)^2
      + sum {i in 1..nx-1} (x[i,ny] - 1)^2
      + sum {j in 1..ny-1} (y[nx,j] - 1)^2
      ) / 2;

   con con1 {i in 2..nx-1, j in 2..ny-1}:
      (x[i,j] - x[i-1,j]) + (y[i,j] - y[i,j-1]) = 1;
   con con2 {i in 2..nx-1}:
      x[i,0] + (x[i,1] - x[i-1,1]) + y[i,1] = 1;
   con con3 {i in 2..nx-1}:
      x[i,ny+1] + (x[i,ny] - x[i-1,ny]) - y[i,ny-1] = 1;
   con con4 {j in 2..ny-1}:
      y[0,j] + (y[1,j] - y[1,j-1]) + x[1,j] = 1;
   con con5 {j in 2..ny-1}:
      y[nx+1,j] + (y[nx,j] - y[nx,j-1]) - x[nx-1,j] = 1;

   for {i in 1..nx-1} x[i,ny].lb = 1;
   for {j in 1..ny-1} y[nx,j].lb = 1;

   solve with nlp;
quit;