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XLeratorDB/math Documentation

SQL Server NLMIN function


NLMIN
Updated: 14 July 2020

Use the table-valued function NLMIN to find the minimum of a function using the Nelder-Mead method.

Syntax
SELECT * FROM [wct].[NLMIN] (
   <@Func, nvarchar(max),>
  ,<@VarNames, nvarchar(max),>
  ,<@StartVals, nvarchar(max),>
  ,<@ReqMin, float,>
  ,<@StepVals, nvarchar(max),>
  ,<@konvge, int,>
  ,<@kcount, int,>)
Arguments
Input NameDescription
@FuncThe function to be evaluated, as a string. The function must be in the form of a SELECT statement.
@VarNamesThe names of the variables
@StartValsThe starting point for the minimization
@ReqMinThe required minimum value
@StepValsStep size for each variable
@konvgeThe convergence check is carried out every KONVGE iterations
@kcountThe maximum number of function evaluations
Return Type
TABLE (
    [VarName] [nvarchar](max) NULL,
    [val] [float] NULL
)
Remarks
  • The returned table includes the variable names and values which are estimated to minimize the function.
  • If @Func is not a valid SELECT statement then NULL is returned.
  • The returned table includes the variable YNEWLO which was the minimum value calculated.
  • The retuned table includes ICOUNT, the number of function evaluations.
  • The returned table include NUMRES, the number of restarts.
  • The retuned table include IFAULT, and error indicator
  • 0 — no errors detected
  • 1 — @ReqMin, @StartVals or @konvge has an illegal value
  • 2 — iteration was terminated because @kcount was exceeded without convergence.
Examples
Example #1

Calculate the minimum of

Our initial estimate is (3,-1,0,1).

DECLARE @func as varchar(max) = N'
SELECT
    POWER(@x1+10*@x2,2)
    +5*POWER(@x3-@x4,2)
    +POWER(@x2 - 2*@x3,4)
    +10*POWER(@x1 - @x4, 4)';
DECLARE @varnames as varchar(max) = N'@x1,@x2,@x3,@x4';
DECLARE @startvals as varchar(max) = N'3.0,-1.0,0.0,1.0';
DECLARE @reqmin as float = 1e-08;
DECLARE @stepvals as varchar(max) = N'1.0,1.0,1.0,1.0';
DECLARE @konvge as int = 10;
DECLARE @kcount as int = 500;
 
SELECT
    VarName,
    val
FROM
    wct.NLMIN(
        @func,
        @varnames,
        @startvals,
        @reqmin,
        @stepvals,
        @konvge,
        @kcount
        );

This produces the following result.

See Also


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