The NLP Procedure

Example 4.2: Using the INQUAD= Option

This example illustrates the INQUAD= option for specifying a quadratic programming problem:

Suppose that , and , , and .

You specify the constant and the Hessian in the data set QUAD1. Notice that the _TYPE_ variable contains the keywords that identify how the procedure should interpret the observations.

  
    data quad1; 
       input _type_ $ _name_ $ x1 x2; 
       datalines; 
    const   .   -100  -100 
    quad   x1    0.4     0 
    quad   x2      0     4 
    ;
 

You specify the QUAD1 data set with the INQUAD= option. Notice that the names of the variables in the QUAD1 data set and the _NAME_ variable match the names of the parameters in the PARMS statement.

  
    proc nlp inquad=quad1 all; 
       min ; 
       parms x1 x2 = -1; 
       bounds  2 <= x1 <= 50, 
             -50 <= x2 <= 50; 
       lincon 10 <= 10 * x1 - x2; 
    run;
 

Alternatively, you can use a sparse format for specifying the matrix, eliminating the zeros. You use the special variables _ROW_, _COL_, and _VALUE_ to give the nonzero row and column names and value.

  
    data quad2; 
       input _type_ $ _row_ $ _col_ $ _value_; 
       datalines; 
    const  .      .    -100 
    quad   x1    x1     0.4 
    quad   x2    x2       4 
    ;
 

You can also include the constraints in the QUAD data set. Notice how the _TYPE_ variable contains keywords that identify how the procedure is to interpret the values in each observation.

  
    data quad3; 
       input _type_ $ _name_ $ x1   x2   _rhs_; 
       datalines; 
    const      .     -100  -100   . 
    quad       x1    0.02     0   . 
    quad       x2    0.00     2   . 
    parms      .       -1    -1   . 
    lowerbd    .        2   -50   . 
    upperbd    .       50    50   . 
    ge         .       10    -1  10 
    ;
 

  
    proc nlp inquad=quad3; 
       min ; 
       parms x1 x2; 
    run;