$title "Test for EMPs AdjustEqu/NYslp option" (EMPADJ01,SEQ=441)

$onText

Test EMP's option AdjustEqu NYslp which adds a slack variable to every
nonlinear equation. Each slacks is multiplied with a penalty variable and added
to the added to / subtracted from the objective.

Contributor: Jan-H. Jagla, April 2009

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variable x1,x2,y;
equation objequ, e1, e2;

objequ.. y =e= 2*x1 + x2;
e1.. x1*x1 + x2*x2 =l= 25;
e2.. x1*x1 - x2*x2 =l= 7;

model m /all/;

$echo Adjustequ NYslp > "%emp.info%"

$onEcho > jams.opt
FileName slpexample.gms
*SubSolver nyslp
SubSolver conopt
Dict slpdict.txt
$offEcho

m.optfile=1;
solve m max y using emp;

execute 'sed "2d" slpexample.gms > slpexample_mod.gms';
execute 'diff -I reslim -bw slpexample_mod.gms slp_ref.gms'
abort$errorlevel 'slpexample_mod.gms and slp_ref.gms differ';

execute 'sed "1d" slpdict.txt > slpdict_mod.txt';
execute 'diff -bw slpdict_mod.txt slpdict_ref.txt'
abort$errorlevel 'slpdict_mod.txt and slpdict_ref.txt differ';

$onEcho > slp_ref.gms
***********************************************
* for more information use JAMS option "Dict"
***********************************************

Variables  x1,x2,objvar,w2,w3,p2,p3,w4;

Positive Variables  w2,w3;

Equations  e1,e2,e3,e4;

e1..  - 2*x1 - x2 + objvar =E= 0 - w4;

e2.. x1*x1 + x2*x2 =L= 25 + w2;

e3.. x1*x1 - x2*x2 =L= 7 + w3;

* e4 defines penalty aggregation variable w4
e4.. w4 =E= + p2*w2 + p3*w3;

* set non-default bounds
p2.fx = 0.0;
p3.fx = 0.0;

Model m / all /;

m.limrow=0; m.limcol=0;

* Index of first slack variable
m.integer1   = 4;
* Index of first penalty variable
m.integer2   = 6;
* Index of penalty aggregation variable
m.integer3   = 8;

Solve m using DNLP maximizing objvar;
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$onEcho > slpdict_ref.txt

********************************************************************************
 Contents
 1 Content of EMP Information File
 2 Processed EMP Information
 3 Dictionary
  3.1 Constraints
  3.2 Variables
********************************************************************************

 1 Content of EMP Information File
 ---------------------------------

     1: Adjustequ NYslp

 2 Processed EMP Information
 ---------------------------

   Number of adjusted constraints specified = 2
   Equ       Type   Weight   Parameters ...
    e2      NYslp       p2
    e3      NYslp       p3

   Thetafunction Counts
     2 NYslp

 3 Dictionary
 ------------
  3.1 Constraints
  ---------------

                  e1  objequ
                  e2  e1
                  e3  e2
                  e4  {new: defines penalty aggregation variable w4}

  3.2 Variables
 --------------

                  x1  x1
                  x2  x2
              objvar  y
                  w2  {new: slack variable of equation e2}
                  w3  {new: slack variable of equation e3}
                  p2  {new: penalty variable for equation e2}
                  p3  {new: penalty variable for equation e3}
                  w4  {new: penalty aggregation variable}
$offEcho