/********************************************************
BCL Example Problems
====================
file xbrecurs.c
```````````````
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
********************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "xprb.h"
#include "xprs.h"
#define T 6
/****DATA****/
double X = 0.00; /* An INITIAL GUESS as to interest rate x */
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) */
double P[] = {-1000, 0, 0, 0, 0, 0}; /* Payments */
double R[] = {206.6, 206.6, 206.6, 206.6, 206.6, 0}; /* " */
double V[] = {-2.95, 0, 0, 0, 0, 0}; /* " */
XPRBvar b[T]; /* Balance */
XPRBvar x; /* Interest rate */
XPRBvar dx; /* Change to x */
XPRBctr interest[T], ctrd;
/***********************************************************************/
void modfinnlp(XPRBprob prob)
{
XPRBvar i[T]; /* Interest */
XPRBvar n[T]; /* Net */
XPRBvar epl[T], emn[T]; /* + and - deviations */
XPRBctr cobj, bal, net;
int t;
/****VARIABLES****/
for(t=0;t<T;t++)
{
i[t]=XPRBnewvar(prob,XPRB_PL, "i", 0, XPRB_INFINITY);
n[t]=XPRBnewvar(prob,XPRB_PL, "n", -XPRB_INFINITY, XPRB_INFINITY);
b[t]=XPRBnewvar(prob,XPRB_PL, "b", -XPRB_INFINITY, XPRB_INFINITY);
epl[t]=XPRBnewvar(prob,XPRB_PL, "epl", 0, XPRB_INFINITY);
emn[t]=XPRBnewvar(prob,XPRB_PL, "emn", 0, XPRB_INFINITY);
}
x=XPRBnewvar(prob,XPRB_PL, "x", 0, XPRB_INFINITY);
dx=XPRBnewvar(prob,XPRB_PL, "dx", -XPRB_INFINITY, XPRB_INFINITY);
XPRBfixvar(i[0],0);
XPRBfixvar(b[T-1],0);
/****OBJECTIVE****/
cobj = XPRBnewctr(prob,"OBJ",XPRB_N); /* Objective: get feasible */
for(t=0;t<T;t++)
{
XPRBaddterm(cobj,epl[t],1);
XPRBaddterm(cobj,emn[t],1);
}
XPRBsetobj(prob,cobj); /* Select objective function */
XPRBsetsense(prob,XPRB_MINIM); /* Choose the sense of the optimization */
/****CONSTRAINTS****/
for(t=0;t<T;t++)
{
net=XPRBnewctr(prob,"net", XPRB_E); /* net = payments - interest */
XPRBaddterm(net, NULL, P[t]+R[t]+V[t]);
XPRBaddterm(net, n[t], 1);
XPRBaddterm(net, i[t], 1);
bal=XPRBnewctr(prob,"bal", XPRB_E); /* Money balance across periods */
XPRBaddterm(bal, b[t], 1);
if(t>0) XPRBaddterm(bal, b[t-1], -1);
XPRBaddterm(bal, n[t], 1);
}
for(t=1;t<T;t++)
{ /* i(t) = (92/365)*( b(t-1)*X + B(t-1)*dx ) approx. */
interest[t]=XPRBnewctr(prob,"int", XPRB_E);
XPRBaddterm(interest[t], i[t], -(365/92.0));
XPRBaddterm(interest[t], b[t-1], X);
XPRBaddterm(interest[t], dx, B[t-1]);
XPRBaddterm(interest[t], epl[t], 1);
XPRBaddterm(interest[t], emn[t], -1);
}
ctrd=XPRBnewctr(prob,"def", XPRB_E); /* X + dx = x */
XPRBaddterm(ctrd, NULL, X);
XPRBaddterm(ctrd, x, 1);
XPRBaddterm(ctrd, dx, -1);
}
/**************************************************************************/
/* Recursion loop (repeat until variation of x converges to 0): */
/* save the current basis and the solutions for variables b[t] and x */
/* set the balance estimates B[t] to the value of b[t] */
/* set the interest rate estimate X to the value of x */
/* reload the problem and the saved basis */
/* solve the LP and calculate the variation of x */
/**************************************************************************/
void solvefinnlp(XPRBprob prob)
{
XPRBbasis basis;
double variation=1.0, oldval, BC[T], XC;
int t, ct=0;
XPRSsetintcontrol(XPRBgetXPRSprob(prob), XPRS_CUTSTRATEGY, 0);
/* Switch automatic cut generation off */
XPRBlpoptimize(prob,""); /* Solve the LP-problem */
while(variation>0.000001)
{
ct++;
basis=XPRBsavebasis(prob); /* Save the current basis */
/* Get the solution values for b and x */
for(t=1;t<T;t++) BC[t-1]=XPRBgetsol(b[t-1]);
XC=XPRBgetsol(x);
printf("Loop %d: %s:%g (variation:%g)\n", ct, XPRBgetvarname(x),
XPRBgetsol(x),variation);
for(t=1;t<T;t++) /* Change coefficients in interest[t] */
{
XPRBsetterm(interest[t], dx, BC[t-1]);
B[t-1]=BC[t-1];
XPRBsetterm(interest[t], b[t-1], XC);
}
XPRBsetterm(ctrd, NULL, XC); /* Change constant term of ctrd */
X=XC;
oldval=XC;
XPRBloadmat(prob); /* Reload the problem */
XPRBloadbasis(basis); /* Load the saved basis */
XPRBdelbasis(basis); /* No need to keep the basis any longer */
XPRBlpoptimize(prob,""); /* Solve the LP-problem */
variation=fabs(XPRBgetsol(x)-oldval);
}
printf("Objective: %g\n", XPRBgetobjval(prob)); /* Get objective value */
printf("Interest rate: %g%%\nBalances: ", XPRBgetsol(x)*100);
for(t=0;t<T;t++) /* Print out the solution values */
printf("%s:%g ", XPRBgetvarname(b[t]), XPRBgetsol(b[t]));
printf("\n");
}
/***********************************************************************/
int main(int argc, char **argv)
{
XPRBprob prob;
prob=XPRBnewprob("Fin_nlp"); /* Initialize a new problem in BCL */
modfinnlp(prob); /* Model the problem */
solvefinnlp(prob); /* Solve the problem */
return 0;
}
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