[R] optimization problem

[tedzzx]

Hi, all

I am facing an optimization problem. I am using the function optim(par,fun),
but I find that every time I give different original guess parameter, I can
get different result. For example
I have a data frame named data:
head(data)
   price     s     x         t
1 1678.0 12817 11200 0.1495902
2 1675.5 12817 11200 0.1495902
3 1678.0 12817 11200 0.1495902
4 1688.0 12817 11200 0.1495902
5 1677.0 12817 11200 0.1495902
6 1678.5 12817 11200 0.1495902
…….
…….
…….

f<-function(p,...){
	v=exp(p[1]+p[2]*(x/s)+p[3]*(x/s)^2)
	d1=(log(s/x)+(v^2)*t/2)/(v*sqrt(t))
	d2=(log(s/x)-(v^2)*t/2)/(v*sqrt(t))
	sum((price-(s*pnorm(d1)-x*pnorm(d2)))^2)
}
p=c(-0.1,-0.1,0.01)
optim(par=p,f) # use the default algorism 

$par
[1] -1.2669459  0.4840307 -0.6607008

$value
[1] 14534.56

$counts
function gradient 
     154       NA 

$convergence
[1] 0

If I try a different original guess estimes, I can get different number
> p=c(-1,-0.1,0.5)
> optim(par=p,f)
$par
[1] -0.7784273 -0.4776970 -0.1877029

$value
[1] 14292.19

$counts
function gradient 
      76       NA 

$convergence
[1] 0

$message
NULL

I have other different original estimes, It also show me different result.

Why?

Thanks.


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