[R] optimization problem

[John C Nash]

tedzxx asked about apparent multiple optima. See below.

Users should be aware that optim() does local optimization. The default Nelder-Mead approach is fairly robust at finding such a local minimum, though it may halt if it is on a flat area of the loss function surface. I would recommend trying one of the BFGS codes (they use somewhat different approaches) and look at the gradient information. With only 3 parameters, these should work fine. There is also another package (I forget the name -- someone?) that does full Newton with Hessian computed. That may be worth using to get more complete information about your problem.

tedzxx: If you send me the data off-list (maybe also include the function again to save me digging it up again), I'll try to provide more information. 

John Nash





>Date: Thu, 27 Nov 2008 23:30:56 -0800 (PST)
>From: tedzzx <zengzhenxing at gmail.com>
>Subject: [R]  optimization problem
>To: r-help at r-project.org
>Message-ID: <20730032.post at talk.nabble.com>
>Content-Type: text/plain; charset=UTF-8


  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)+(v2)*t/2)/(v*sqrt(t))
	d2=(log(s/x)-(v2)*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 


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

  Why?

Thanks.