Question

I am new to C.

I am trying to use optim function from C. According to “Writing R Extension” Section 5.8, the Nelder Mead method requires 16 arguments:

void nmmin(int n, double *xin, double *x, double *Fmin, optimfn fn,
           int *fail, double abstol, double intol, void *ex,
           double alpha, double beta, double gamma, int trace,
           int *fncount, int maxit);

In my understanding, unlike R which accepts default values in arguments of functions, C requires users of the function to provide all the arguments.
Although I read optim hep page, I still have troubles understanding the meaning of some of these arguments i.e.:

• fail
• intol
• ex
• fncount

I highly appreciate if anyone can direct me where the descriptions of all the arguments are.

p.s.

The followings are the arguments that I figure out what they are:

• n: the number of parameters,
• xin: the initial value of the parameter
• x: storage for the final parameters on exit, with fi
• Fmin: the final value of the objective function
• fn: the objective function
• abstol: absolute tolerance
• maxit: the maximum number of iterations
• trace: Non-negative integer. If positive, tracing information on the progress of the optimization is produced.

The followings are some arguments specific for the Nelder Mead method:

• alpha: R optim function uses = 1

• beta: R optim function uses = 0.5

• gamma: R optim function uses = 2
  (I found these default values by reading the optim function codes)

Answer 1

fail – receives true if the function failed

intol – user-initialized conversion tolerance

ex – data to pass to the optimization function (fn)

alpha – reflection factor

beta – contraction and reduction factor

gamma – extension factor

fncount – receives the number of times the optimization function was called in the iteration loop

You can see how these parameters are used here:

http://fossies.org/dox/R-2.15.1/optim_8c_source.html#l00674

For instance, intol is used like so:

convtol = intol * (fabs(f) + intol);
if (trace) Rprintf("  Scaled convergence tolerance is %g\n", convtol);

There are some more details about the Nelder-Mead algorithm here, with Pascal code:

http://books.google.com/books?id=M9hTn3UAheQC&pg=PA173

(Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation by John C. Nash)