INTERFACE JSUniMin;

(*
  An ad-hoc algorithm for minimizing a univariate function
  without derivatives.

  Created by J.Stolfi on May-Jul 1994.
*)

IMPORT UniMin;

TYPE 
  T <: Public;
  Public = UniMin.T OBJECT METHODS

      setAlpha(alpha: LONGREAL): T;
        (*
          Sets the ``venture risk factor''. 
          "alpha = 1" gives strict golden bissection search;
          "alpha < 1" uses parabolic fitting, at the cost of
          possibly slower convergence in the worst case. *)
    END;
    (*
      The "minimize" method does not use the derivative provided
      by "eval", and works only with the function values.  It looks
      for three points "u", "z", "v" in the given interval "[a__b]"
      such that

        1. The points are ordered and not too close:
            "u + delta <= z <= v - delta"
        3. They bracket at lest one local minimum:
            "F(z) <= MIN(F(u), F(v))"
        4. The gaps can't be split any further:
            "MAX(z-u, v-z) < 2*delta"
            
      where "delta = tol + sqrt(machinePrecision)*ABS(z)"
            
      When such a triple is found, or when either "eval" or "check"
      return "TRUE", "minimize" returns in "fx" the smallest of
      "F(u)" "F(z)", and "F(w)", and in "x" the corresponding
      argument.
  *)
  
END JSUniMin.