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.TH optim G "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
optim - non-linear optimization routine
.SH CALLING SEQUENCE
.nf
[f,xopt]=optim(costf,x0)
[f,[xopt,[gradopt,[work]]]]=optim(costf,[contr],x0,['algo'],[df0,[mem]],
[work],[stop],['in'],[imp=iflag])
.fi
.SH PARAMETERS
.TP 10
costf
: external, i.e Scilab function or string (\fVcostf\fR is the cost function: see below its
calling sequence (Scilab or Fortran)).
.TP
x0
: real vector (initial value of variable to be minimized).
.TP
f
: value of optimal cost (\fVf=costf(xopt)\fR)
.TP
xopt
: best value of \fVx\fR found.
.TP
contr
: \fV'b',binf,bsup\fR with \fVbinf\fR and \fVbsup\fR real vectors with same
dimension as \fVx0\fR. \fVbinf\fR and \fVbsup\fR are lower and upper bounds on \fVx\fR.
.TP
"algo"
: \fV'qn'\fR or \fV'gc'\fR or \fV'nd'\fR . This string stands for quasi-Newton (default),
conjugate gradient or non-differentiable respectively.
Note that \fV'nd'\fR does not accept bounds on \fVx\fR ).
.TP
df0
: real scalar. Guessed decreasing of \fVf\fR at first iteration.
(\fVdf0=1\fR is the default value).
.TP
mem :
integer, number of variables used to approximate the
Hessian, (\fValgo='gc' or 'nd'\fR). Default value is around 6.
.TP
stop
: sequence of optional parameters controlling the
convergence of the algorithm.
\fV
stop= 'ar',nap, [iter [,epsg [,epsf [,epsx]]]]\fR
.RS
.TP
"ar"
: reserved keyword for stopping rule selection defined as follows:
.TP
nap
: maximum number of calls to \fVcostf\fR allowed.
.TP
iter
: maximum number of iterations allowed.
.TP
epsg
: threshold on gradient norm.
.TP
epsf
: threshold controlling decreasing of \fVf\fR
.TP
epsx
: threshold controlling variation of \fVx\fR.
This vector (possibly matrix) of same size as \fVx0\fR can be used
to scale \fVx\fR.
.RE
.TP
"in"
: reserved keyword for initialization of parameters
used when \fVcostf\fR in given as a Fortran routine (see below).
.TP
"imp=iflag"
: named argument used to set the trace mode. \fViflag=0\fR nothing
(execpt errors) is reported, \fViflag=1\fR initial and final reports,
\fViflag=2\fR adds a report per iteration, \fViflag>2\fR add reports on
linear search. Warning, most of these reports are written on the
Scilab standard output.
.TP
gradopt
: gradient of \fVcostf\fR at \fVxopt\fR
.TP
work
: working array for hot restart for quasi-Newton method.
This array is automatically initialized by \fVoptim\fR when
\fVoptim\fR is invoked. It can be used as input parameter to
speed-up the calculations.
.SH DESCRIPTION
Non-linear optimization routine for programs without constraints or with bound constraints:
.nf
min costf(x) w.r.t x.
.fi
\fVcostf\fR is an "external" i.e function, or list or Fortran routine (see "external").
This external must return \fVf\fR (\fVcostf(x)\fR) and \fVg\fR (gradient of \fVcostf\fR)
given \fVx\fR.
.LP
If \fVcostf\fR is a function, the calling sequence for \fVcostf\fR must be:
.nf
[f,g,ind]=costf(x,ind).
.fi
Here, \fVcostf\fR is a function which returns \fVf\fR, value (real number) of
cost function at \fVx\fR, and \fVg\fR, gradient vector of cost function at \fVx\fR.
The variable \fVind\fR is used by \fVoptim\fR and is described below.
.LP
If \fVind=2\fR (resp. \fV3, 4\fR), \fVcostf\fR must provide \fVf\fR (resp. \fVg, f\fR and \fVg\fR).
.LP
If \fVind=1\fR nothing is computed (used for display purposes only).
.LP
On output, \fVind<0\fR means that \fVf\fR cannot be evaluated at \fVx\fR and
\fVind=0\fR interrupts the optimization.
.LP
If \fVcostf\fR is a character string, it refers to the name of a Fortran routine
which must be linked to Scilab (see examples in the routines \fVfoptim.f\fR
and e.g. \fVgenros.f\fR in the directory SCIDIR/default)
.LP
Dynamic link of Fortran routine is also possible (help \fVlink\fR).
.LP
Here, the generic calling sequence for the Fortran subroutine is:
\fVfunction costf(ind,n,x,f,g,ti,tr,td)\fR
.LP
\fVind\fR has the same meaning as above if set to \fV0,1,2\fR but the
values \fVind=10\fR and \fVind=11\fR are now valid.
These values are used for initializations (see below).
.LP
\fVn\fR is the dimension of \fVx\fR, \fVx\fR is an \fVn\fR vector,
\fVti,tr,td\fR are working arrays.
.LP
The Fortran function \fVcostf\fR must return \fVf\fR and the vector \fVg\fR,
given \fVx, ind, n, ti, tr, td\fR.
.LP
If \fVcostf\fR is given as a Fortran routine, it is possible to initialize
parameters or to send Scilab variables to this routine.
.LP
This facility is managed by the parameter \fV'in\fR.
.LP
If the string \fV'in'\fR is present, initialization is done by Fortran:
\fVoptim\fR makes two calls to the Fortran function \fVcostf\fR, once with
\fVind=10\fR and once with \fVind=11\fR. In this case, for \fVind=10\fR,
\fVcostf\fR must set the dimensions \fVnti, ntr, ntd\fR of \fVti, tr, td\fR
in the \fVcommon/nird/nti, ntr, ntd\fR and, for \fVind=11\fR, \fVcostf\fR
must initialize the vectors \fVti , tr, td\fR (integer vector, real vector,
double precision vector respectively).
.LP
In the calling sequence of \fVoptim\fR, the string \fV'in'\fR can be
replaced by \fV'ti', valti ,'td' , valtd\fR. Then, the Fortran function
\fVcostf(ind, x, f, g, ti, tr, td)\fR is evaluated with \fVti=valti\fR
and \fVtd=valtd\fR whatever the value of \fVind\fR.
Thus, the Scilab variables \fVvalti\fR and \fVvaltd\fR (integer vector and
real vector) are sent to the Fortran function \fVcostf\fR.
.LP
It is also possible to save the content of of the working arrays
\fVti\fR and \fVtd\fR. This is possible by adding the strings 'si' and/or 'sd'
at the ned of the calling sequence of \fVoptim\fR.
Then, the output variables must be: \fV[f,[x,[g],[to]]],[ti],[td]]\fR.
.SH EXAMPLES
.nf
xref=[1;2;3];x0=[1;-1;1]
deff('[f,g,ind]=cost(x,ind)','f=0.5*norm(x-xref)^2,g=x-xref');
[f,xopt]=optim(cost,x0) //Simplest call
[f,xopt,gopt]=optim(cost,x0,'gc') // By conjugate gradient
[f,xopt,gopt]=optim(cost,x0,'nd') //Seen as non differentiable
[f,xopt,gopt]=optim(cost,'b',[-1;0;2],[0.5;1;4],x0) // Bounds on x
[f,xopt,gopt]=optim(cost,'b',[-1;0;2],[0.5;1;4],x0,'gc') // Bounds on x
[f,xopt,gopt]=optim(cost,'b',[-1;0;2],[0.5;1;4],x0,'gc','ar',3)
// Here, 3 calls to cost are allowed.
// Now calling the Fortran subroutine "genros" in SCIDIR/default/Ex-optim.f
// See also the link function for dynamically linking an objective function
[f,xopt,gopt]=optim('genros',[1;2;3]) //Rosenbrock's function
.fi
.SH SEE ALSO
external, quapro, linpro, datafit, leastsq
|
