/********************************************************
  Xpress-BCL Java Example Problems
  ================================

  file xbqpr12.java
  `````````````````
  Small Quadratic Programming example.
       minimize x1 + x1^2 +2x1x2 +2x2^2 +x4^2
       s.t. C1:  x1 +2x2 -4x4 >= 0
            C2: 3x1 -2x3 - x4 <= 100
            C3: 10 <= x1 +3x2 +3x3 -2x4 <= 30
            0<=x1<=20
            0<=x2,x3
            x4 free

  (c) 2008 Fair Isaac Corporation
      author: S.Heipcke, Jan. 2000, rev. Dec. 2011
********************************************************/

import java.io.*;
import com.dashoptimization.*;

public class xbqpr12
{
 static final int NXPRBvar = 4;

/***********************************************************************/

 public static void main(String[] args) throws IOException
 {
  XPRB bcl;
  XPRBctr c;
  XPRBexpr le, qobj;
  XPRBvar[] x;
  int i;
  XPRBprob p;
  
  bcl = new XPRB();               /* Initialize BCL */
  p = bcl.newProb("QPr12");       /* Create a new problem in BCL */

/**** VARIABLES ****/
  x = new XPRBvar[NXPRBvar];
  x[0] = p.newVar("x1", XPRB.PL, 0, 20);
  x[1] = p.newVar("x2");
  x[2] = p.newVar("x3");
  x[3] = p.newVar("x4", XPRB.PL, -XPRB.INFINITY, XPRB.INFINITY);

/****OBJECTIVE****/
  qobj = new XPRBexpr();          /* Define the objective function */
  qobj.add(x[0]);
  qobj.add( (x[0].sqr()) .add(x[0].mul(2).mul(x[1]))
   .add(x[1].sqr().mul(2)) .add(x[3].sqr()) );
  p.setObj(qobj);
 
/**** CONSTRAINTS ****/
  p.newCtr("C1", x[0].add(x[1].mul(2)).add(x[3].mul(-4)) .gEql(0) );
  p.newCtr("C2", x[0].mul(3).add(x[2].mul(-2)).add(x[3].mul(-1)) .lEql(100) );
  c = p.newCtr("C3", x[0].add(x[1].mul(3)) .add(x[2].mul(3)) 
      .add(x[3].mul(-2)) );
  c.setRange(10,30);
   
/****SOLVING + OUTPUT****/
  p.print();			  /* Print out the problem definition */
  p.exportProb(XPRB.MPS,"QPr12"); /* Output the matrix in MPS format */
  p.exportProb(XPRB.LP,"QPr12");  /* Output the matrix in LP format */
  
  p.setSense(XPRB.MINIM);         /* Choose the sense of the  optimization */   
  p.lpOptimize("");               /* Solve the QP-problem */

  System.out.println("Objective function value: " + p.getObjVal());
  for(i=0;i<NXPRBvar;i++)
   System.out.print(x[i].getName() + ": " +  x[i].getSol() + ", ");
  System.out.println();


  p.finalize();                   /* Delete the problem */      
  p=null;
 } 
}