From: ted.dunning@gmail.com   
      
   > Imagine a general heuristic problem.   
      
   It sounds to me like your definition of heuristic is different from the   
   standard definition.   
      
   > In general, as one increases the number of variables that need to be   
   optimized, the   
   > number of local optima in this optimization surface increases.   
      
   This definitely *can* happen, but it definitely does not happen in   
   general.  Consider the quadratic bowl, \sum x_i^2.  The number of local   
   minima is one (i.e. the global minimum) for any dimensionality number   
   of x_i's.   
      
   I think perhaps you are confusing the issue of multiple local minima   
   with the so-called curse of dimensionality which has more to do with   
   over-fitting than with the number of local minima.  Over-fitting is due   
   to trying to fit noisy data with a model that has too many free   
   parameters.  The critical value of "too many" is the key problem and   
   that has to do with things like generalization and empirical risk, not   
   local minima.   
      
   Can you say more about what you are really asking about?   
      
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