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/* lbfgsb-example1.f -- translated by f2c (version 20050501).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "v3p_netlib.h"
/* DRIVER 1 */
/* -------------------------------------------------------------- */
/* SIMPLE DRIVER FOR L-BFGS-B (version 2.1) */
/* -------------------------------------------------------------- */
/* L-BFGS-B is a code for solving large nonlinear optimization */
/* problems with simple bounds on the variables. */
/* The code can also be used for unconstrained problems and is */
/* as efficient for these problems as the earlier limited memory */
/* code L-BFGS. */
/* This is the simplest driver in the package. It uses all the */
/* default settings of the code. */
/* References: */
/* [1] R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, ``A limited */
/* memory algorithm for bound constrained optimization'', */
/* SIAM J. Scientific Computing 16 (1995), no. 5, pp. 1190--1208. */
/* [2] C. Zhu, R.H. Byrd, P. Lu, J. Nocedal, ``L-BFGS-B: FORTRAN */
/* Subroutines for Large Scale Bound Constrained Optimization'' */
/* Tech. Report, NAM-11, EECS Department, Northwestern University, */
/* 1994. */
/* (Postscript files of these papers are available via anonymous */
/* ftp to eecs.nwu.edu in the directory pub/lbfgs/lbfgs_bcm.) */
/* * * * */
/* NEOS, November 1994. (Latest revision June 1996.) */
/* Optimization Technology Center. */
/* Argonne National Laboratory and Northwestern University. */
/* Written by */
/* Ciyou Zhu */
/* in collaboration with R.H. Byrd, P. Lu-Chen and J. Nocedal. */
/* NOTE: The user should adapt the subroutine 'timer' if 'etime' is */
/* not available on the system. An example for system */
/* AIX Version 3.2 is available at the end of this driver. */
/* ************** */
/*< program driver >*/
/* Main program */ int main()
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_cmp(char *, char *, ftnlen, ftnlen);
/* Local variables */
doublereal f, g[1024];
integer i__;
doublereal l[1024];
integer m, n;
doublereal u[1024], x[1024], t1, t2, wa[42584];
integer nbd[1024], iwa[3072];
char task[60];
doublereal factr;
char csave[60];
doublereal dsave[29];
integer isave[44];
logical lsave[4];
doublereal pgtol;
integer iprint;
/* This simple driver demonstrates how to call the L-BFGS-B code to */
/* solve a sample problem (the extended Rosenbrock function */
/* subject to bounds on the variables). The dimension n of this */
/* problem is variable. */
/*< integer nmax, mmax >*/
/*< parameter (nmax=1024, mmax=17) >*/
/* nmax is the dimension of the largest problem to be solved. */
/* mmax is the maximum number of limited memory corrections. */
/* Declare the variables needed by the code. */
/* A description of all these variables is given at the end of */
/* the driver. */
/*< character*60 task, csave >*/
/*< logical lsave(4) >*/
/*< >*/
/*< >*/
/* Declare a few additional variables for this sample problem. */
/*< double precision t1, t2 >*/
/*< integer i >*/
/* We wish to have output at every iteration. */
/*< iprint = 1 >*/
iprint = 1;
/* We specify the tolerances in the stopping criteria. */
/*< factr=1.0d+7 >*/
factr = 1e7;
/*< pgtol=1.0d-5 >*/
pgtol = 1e-5;
/* We specify the dimension n of the sample problem and the number */
/* m of limited memory corrections stored. (n and m should not */
/* exceed the limits nmax and mmax respectively.) */
/*< n=25 >*/
n = 25;
/*< m=5 >*/
m = 5;
/* We now provide nbd which defines the bounds on the variables: */
/* l specifies the lower bounds, */
/* u specifies the upper bounds. */
/* First set bounds on the odd-numbered variables. */
/*< do 10 i=1,n,2 >*/
i__1 = n;
for (i__ = 1; i__ <= i__1; i__ += 2) {
/*< nbd(i)=2 >*/
nbd[i__ - 1] = 2;
/*< l(i)=1.0d0 >*/
l[i__ - 1] = 1.;
/*< u(i)=1.0d2 >*/
u[i__ - 1] = 100.;
/*< 10 continue >*/
/* L10: */
}
/* Next set bounds on the even-numbered variables. */
/*< do 12 i=2,n,2 >*/
i__1 = n;
for (i__ = 2; i__ <= i__1; i__ += 2) {
/*< nbd(i)=2 >*/
nbd[i__ - 1] = 2;
/*< l(i)=-1.0d2 >*/
l[i__ - 1] = -100.;
/*< u(i)=1.0d2 >*/
u[i__ - 1] = 100.;
/*< 12 continue >*/
/* L12: */
}
/* We now define the starting point. */
/*< do 14 i=1,n >*/
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< x(i)=3.0d0 >*/
x[i__ - 1] = 3.;
/*< 14 continue >*/
/* L14: */
}
/*< write (6,16) >*/
/*
16 format(/,5x, 'Solving sample problem.',
+ /,5x, ' (f = 0.0 at the optimal solution.)',/)
*/
#if 0
printf(" Solving sample problem.\n"
" (f = 0.0 at the optimal solution.)\n");
#endif
/*< >*/
/* We start the iteration by initializing task. */
/*< task = 'START' >*/
s_copy(task, "START", (ftnlen)60, (ftnlen)5);
/* ------- the beginning of the loop ---------- */
/*< 111 continue >*/
L111:
/* This is the call to the L-BFGS-B code. */
/*< >*/
setulb_(&n, &m, x, l, u, nbd, &f, g, &factr, &pgtol, wa, iwa, task, &
iprint, csave, lsave, isave, dsave);
/*< if (task(1:2) .eq. 'FG') then >*/
if (s_cmp(task, "FG", (ftnlen)2, (ftnlen)2) == 0) {
/* the minimization routine has returned to request the */
/* function f and gradient g values at the current x. */
/* Compute function value f for the sample problem. */
/*< f=.25d0*(x(1)-1.d0)**2 >*/
/* Computing 2nd power */
d__1 = x[0] - 1.;
f = d__1 * d__1 * .25;
/*< do 20 i=2,n >*/
i__1 = n;
for (i__ = 2; i__ <= i__1; ++i__) {
/*< f=f+(x(i)-x(i-1)**2)**2 >*/
/* Computing 2nd power */
d__2 = x[i__ - 2];
/* Computing 2nd power */
d__1 = x[i__ - 1] - d__2 * d__2;
f += d__1 * d__1;
/*< 20 continue >*/
/* L20: */
}
/*< f=4.d0*f >*/
f *= 4.;
/* Compute gradient g for the sample problem. */
/*< t1=x(2)-x(1)**2 >*/
/* Computing 2nd power */
d__1 = x[0];
t1 = x[1] - d__1 * d__1;
/*< g(1)=2.d0*(x(1)-1.d0)-1.6d1*x(1)*t1 >*/
g[0] = (x[0] - 1.) * 2. - x[0] * 16. * t1;
/*< do 22 i=2,n-1 >*/
i__1 = n - 1;
for (i__ = 2; i__ <= i__1; ++i__) {
/*< t2=t1 >*/
t2 = t1;
/*< t1=x(i+1)-x(i)**2 >*/
/* Computing 2nd power */
d__1 = x[i__ - 1];
t1 = x[i__] - d__1 * d__1;
/*< g(i)=8.d0*t2-1.6d1*x(i)*t1 >*/
g[i__ - 1] = t2 * 8. - x[i__ - 1] * 16. * t1;
/*< 22 continue >*/
/* L22: */
}
/*< g(n)=8.d0*t1 >*/
g[n - 1] = t1 * 8.;
/* go back to the minimization routine. */
/*< goto 111 >*/
goto L111;
/*< endif >*/
}
/*< if (task(1:5) .eq. 'NEW_X') goto 111 >*/
if (s_cmp(task, "NEW_X", (ftnlen)5, (ftnlen)5) == 0) {
goto L111;
}
/* the minimization routine has returned with a new iterate, */
/* and we have opted to continue the iteration. */
/* ---------- the end of the loop ------------- */
/* If task is neither FG nor NEW_X we terminate execution. */
/*< stop >*/
/*< end >*/
return 0;
} /* MAIN__ */
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