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

  file xbrecurs.java
  ``````````````````
  Recursion solving a non-linear financial planning problem
  The problem is to solve
  	net(t) = Payments(t)  - interest(t)
  	balance(t) = balance(t-1) - net(t)
  	interest(t) = (92/365) * balance(t) * interest_rate
  where
        balance(0) = 0
        balance[T] = 0
  for interest_rate

  (c) 2008 Fair Isaac Corporation
      author: S.Heipcke, 2001, rev. Mar. 2011
********************************************************/

import java.lang.*;
import com.dashoptimization.*;

public class xbrecurs {
    static final int T=6;

    /****DATA****/
    static double X = 0.00;         /* An INITIAL GUESS as to interest rate x */
    static final double[] B =
        /* {796.35, 589.8918, 398.1351, 201.5451, 0.0, 0.0}; */
    {1,1,1,1,1,1};      /* An INITIAL GUESS as to balances b(t) */
    static final double[] P = {-1000, 0, 0, 0, 0, 0};            /* Payments */
    static final double[] R = {206.6, 206.6, 206.6, 206.6, 206.6, 0}; /*  "  */
    static final double[] V = {-2.95, 0, 0, 0, 0, 0};                 /*  "  */

    static XPRBvar[] b;             /* Balance */
    static XPRBvar x;               /* Interest rate */
    static XPRBvar dx;              /* Change to x */
    static XPRBctr[] interest;
    static XPRBctr ctrd;

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

    static void modFinNLP(XPRBprob p) throws XPRSexception {
        XPRBvar[] i;                   /* Interest */
        XPRBvar[] n;                   /* Net */
        XPRBvar[] epl, emn;            /* + and - deviations */
        XPRBexpr cobj, le;
        int t;

        /****VARIABLES****/
        b = new XPRBvar[T];
        i = new XPRBvar[T];
        n = new XPRBvar[T];
        epl = new XPRBvar[T];
        emn = new XPRBvar[T];
        for(t=0;t<T;t++) i[t]=p.newVar("i"); n[t]=p.newVar("n", b[t]=p.newVar("b", epl[t]=p.newVar("epl"); emn[t]=p.newVar("emn"); x=p.newVar("x"); dx=p.newVar("dx", cobj=new for(t=0;t<T;t++) Objective: get feasible Select objective function Choose the sense of optimization net=payments interest Money balance across periods>0) p.newCtr("bal", b[t].eql(b[t-1].add(n[t].mul(-1))) );
                else  p.newCtr("bal", b[t].eql(n[t].mul(-1)) );
            }

        interest = new XPRBctr[T];
        for(t=1;t<T;t++) i(t)=(92/365)*( approx. interest[t]=p.newCtr("int", ctrd=p.newCtr("def", x=dx X Recursion loop until variation of converges to save the current basis and solutions for variables set balance estimates value interest rate estimate reload problem saved solve LP calculate static void throws XPRSexception XPRBbasis double int ct=0; Switch automatic cut generation off Solve LP-problem BC=new>0) {
            ct++;
            basis=p.saveBasis();           /* Save the current basis */

            /* Get the solution values for b and x */
            for(t=1;t<T;t++) BC[t-1]=b[t-1].getSol();
            XC=x.getSol();
            System.out.println("Loop " + ct + ": " + x.getName() + ":" + x.getSol()
                               + " (variation:" + variation + ")");

            for(t=1;t<T;t++) {                /* Change coefficients in interest[t] */
                interest[t].setTerm(dx, BC[t-1]);
                B[t-1]=BC[t-1];
                interest[t].setTerm(b[t-1], XC);
            }
            ctrd.setTerm(XC);              /* Change constant term of ctrd */
            X=XC;

            oldval=XC;
            p.loadMat();                   /* Reload the problem */
            p.loadBasis(basis);            /* Load the saved basis */
            basis=null;                    /* No need to keep the basis any longer */

            p.lpOptimize("");              /* Solve the LP-problem */
            variation=Math.abs(x.getSol()-oldval);
        }

        System.out.println("Objective: " + p.getObjVal()); /* Get objective value */
        System.out.println("Interest rate: " + x.getSol()*100 + "%");
        System.out.print("Balances:  ");
        for(t=0;t<T;t++)                /* Print out the solution values */
            System.out.print(b[t].getName() + ":" + b[t].getSol() + " ");
        System.out.println();
    }

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

    public static void main(String[] args) throws XPRSprobException, XPRSexception {
        try (XPRBprob p = new XPRBprob("Fin_nlp"); /* Initialize BCL and create a new problem*/
             XPRS xprs = new XPRS()) {             /* Initialize Xpress-Optimizer */
            modFinNLP(p);                    /* Model the problem */
            solveFinNLP(p);                  /* Solve the problem */
        }
    }
}