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XLeratorDB/math Documentation

SQL Server BFGS function


BFGS
Updated: 16 April 2018

Use the scalar function BFGS to find the minimum of a functions using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method.

Syntax
SELECT [wct].[BFGS] (
   <@Func, nvarchar(max),>
  ,<@VarNames, nvarchar(4000),>
  ,<@X, nvarchar(4000),>
  ,<@H, float,>
  ,<@tol, float,>)
Arguments
Input NameDescription
@FuncThe function to be evaluated, as a string. The function must be in the form of a SELECT statement.
@VarNameThe name of the variable
@XThe starting point for the minimization
@HStep size
@tolTolerance (for the solution)
Return Type
[nvarchar](max)
Remarks
  • If @Func returns a NULL then NULL Is returned.
  • If @Func is not a valid SELECT statement then NULL is returned.
  • If no solution is found then NULL is returned.
  • If @X is NULL then @X = ''.
  • If @H is NULL then @H = 0.
  • If @H <= 0 then @H = 2^(-52).
  • If @tol is NULL then @tol = 0.0001
  • Available in XLeratorDB / math 2008 only
Examples
Example #1

Calculate the minimum of

Our initial estimate is the point (0,0).

Since the result is returned as a string, we will use the MATRIX function to unpack the results into a vector format.

SELECT
    *
FROM
    wctMath.wct.MATRIX(
        wct.BFGS(
             'SELECT EXP(@x1-1) + EXP(-@x2+1) + POWER(@x1 - @x2,2)'
            ,'@x1,@x2'
            ,'0,0'
            ,NULL
            ,NULL)
        )

This produces the following result.

See Also


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