ex_3qn3.c

an quasi-newton method used in non-linear programming and especially in optimization

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#include "math_util.h"
int n_fun;
main()
{
    clock_t time_0, time_1;
    long double dtime;
    long double tol, *x;
    int n;
    long double ex3_fun( long double * );
    void q_newton_3( long double(*)(),
                 long double *, int, long double );
    
	n_fun = 0;
	n = 4;
	x = a1d_allo_dbl( n );
	vec_null( x, n );
	tol = 1.0e-4;
	
    time_0 = clock();
    q_newton_3( ex3_fun, x, n, tol );
    time_1 = clock();
    dtime = (long double)(time_1-time_0)/((long double)CLOCKS_PER_SEC);
    
    printf("Solution x: ");print_vec_dbl( x, n );
    printf("\n # of function evaluations: %d\n",n_fun);
    printf(" Solution time: %Le",dtime);
}
/*
	Wood function
*/
long double ex3_fun( x )
long double *x;
{
   long double f, t1, t3, t5, t6, t8, t10, t11, t12, t13, t14, 
               x1, x2, x3, x4;
   
   n_fun++;
   
   x1 = x[0];
   x2 = x[1];
   x3 = x[2];
   x4 = x[3];
   t1 = x1*x1;
   t3 = pow(x2-t1,2.0);
   t5 = pow(1.0-x1,2.0);
   t6 = x3*x3;
   t8 = pow(x4-t6,2.0);
   t10 = pow(1.0-x3,2.0);
   t11 = x2-1.0;
   t12 = t11*t11;
   t13 = x4-1.0;
   t14 = t13*t13;
   f = 100.0*t3+t5+90.0*t8+t10+0.101E2*t12+0.101E2*t14+0.198E2*t11*t13;
     
   return( f );
}
/*
***  Norm( h ) <= eps
Solution x:  1.000000e+00  9.999999e-01  1.000001e+00  1.000002e+00

 # of function evaluations: 1272
 Solution time: 6.833333e+00
 */