GAMS

SET      n /One, Two, Three/
         t /One, Two, Three/;
PARAMETER
   c(n)     /one   5   ,   two   9   ,   three   13/
   q(n)     /one   4   ,   two   3   ,   three 8/;
POSITIVE VARIABLES     x(n,t), mu(n,t), lambda(n,t);
EQUATIONS KKT(n,t), sl(n,t);
KKT(n,t).. 0 =e= c(n) + mu(n,t) + lambda(n,t);
sl(n,t).. 0 =e= mu(n,t)*(x(n,t) - q(n))
MODEL problem /ALL/;
SOLVE problem using MCP;


Output:

GAMS 24.7.4  r58773 Released Sep 19, 2016 WEX-WEI x86 64bit/MS Windows 05/04/18 14:52:16 Page 1
G e n e r a l   A l g e b r a i c   M o d e l i n g   S y s t e m
C o m p i l a t i o n


   1  SET      n /One, Two, Three/
   2           t /One, Two, Three/;
   3  PARAMETER
   4     c(n)     /one   5   ,   two   9   ,   three   13/
   5     q(n)     /one   4   ,   two   3   ,   three 8/;
   6  POSITIVE VARIABLES     x(n,t), mu(n,t), lambda(n,t);
   7  EQUATIONS KKT(n,t), sl(n,t);
   8  KKT(n,t).. 0 =e= c(n) + mu(n,t) + lambda(n,t);
   9  sl(n,t).. 0 =e= mu(n,t)*(x(n,t) - q(n))
  10  MODEL problem /ALL/;
  11  SOLVE problem using MCP;
  12
  13


COMPILATION TIME     =        0.016 SECONDS      3 MB  24.7.4 r58773 WEX-WEI
GAMS 24.7.4  r58773 Released Sep 19, 2016 WEX-WEI x86 64bit/MS Windows 05/04/18 14:52:16 Page 2
G e n e r a l   A l g e b r a i c   M o d e l i n g   S y s t e m
Equation Listing    SOLVE problem Using MCP From line 11


---- KKT  =E=

KKT(One,One)..  - mu(One,One) - lambda(One,One) =E= 5 ; (LHS = 0
     , INFES = 5 ****)

KKT(One,Two)..  - mu(One,Two) - lambda(One,Two) =E= 5 ; (LHS = 0
     , INFES = 5 ****)

KKT(One,Three)..  - mu(One,Three) - lambda(One,Three) =E= 5 ;

      (LHS = 0, INFES = 5 ****)

REMAINING 6 ENTRIES SKIPPED


---- sl  =E=

sl(One,One)..  (0)*x(One,One) + (4)*mu(One,One) =E= 0 ; (LHS = 0)

sl(One,Two)..  (0)*x(One,Two) + (4)*mu(One,Two) =E= 0 ; (LHS = 0)

sl(One,Three)..  (0)*x(One,Three) + (4)*mu(One,Three) =E= 0 ; (LHS = 0)

REMAINING 6 ENTRIES SKIPPED

GAMS 24.7.4  r58773 Released Sep 19, 2016 WEX-WEI x86 64bit/MS Windows 05/04/18 14:52:16 Page 3
G e n e r a l   A l g e b r a i c   M o d e l i n g   S y s t e m
Column Listing      SOLVE problem Using MCP From line 11


---- x

x(One,One)
                (.LO, .L, .UP, .M = 0, 0, +INF, 0)
       (0)      sl(One,One)

x(One,Two)
                (.LO, .L, .UP, .M = 0, 0, +INF, 0)
       (0)      sl(One,Two)

x(One,Three)
                (.LO, .L, .UP, .M = 0, 0, +INF, 0)
       (0)      sl(One,Three)

REMAINING 6 ENTRIES SKIPPED

---- mu

mu(One,One)
                (.LO, .L, .UP, .M = 0, 0, +INF, 0)
       -1       KKT(One,One)
       (4)      sl(One,One)

mu(One,Two)
                (.LO, .L, .UP, .M = 0, 0, +INF, 0)
       -1       KKT(One,Two)
       (4)      sl(One,Two)

mu(One,Three)
                (.LO, .L, .UP, .M = 0, 0, +INF, 0)
       -1       KKT(One,Three)
       (4)      sl(One,Three)

REMAINING 6 ENTRIES SKIPPED

---- lambda

lambda(One,One)
                (.LO, .L, .UP, .M = 0, 0, +INF, 0)
       -1       KKT(One,One)

lambda(One,Two)
                (.LO, .L, .UP, .M = 0, 0, +INF, 0)
       -1       KKT(One,Two)

lambda(One,Three)
                (.LO, .L, .UP, .M = 0, 0, +INF, 0)
       -1       KKT(One,Three)

REMAINING 6 ENTRIES SKIPPED

**** Unmatched variable not free or fixed
     x(One,One)

**** Unmatched variable not free or fixed
     x(One,Two)

**** Unmatched variable not free or fixed
     x(One,Three)

**** Unmatched variable not free or fixed
     x(Two,One)

**** Unmatched variable not free or fixed
     x(Two,Two)

**** Unmatched variable not free or fixed
     x(Two,Three)

**** Unmatched variable not free or fixed
     x(Three,One)

**** Unmatched variable not free or fixed
     x(Three,Two)

**** Unmatched variable not free or fixed
     x(Three,Three)

**** Unmatched variable not free or fixed
     mu(One,One)

**** Unmatched variable not free or fixed
     mu(One,Two)

**** Unmatched variable not free or fixed
     mu(One,Three)

**** Unmatched variable not free or fixed
     mu(Two,One)

**** Unmatched variable not free or fixed
     mu(Two,Two)

**** Unmatched variable not free or fixed
     mu(Two,Three)

**** Unmatched variable not free or fixed
     mu(Three,One)

**** Unmatched variable not free or fixed
     mu(Three,Two)

**** Unmatched variable not free or fixed
     mu(Three,Three)

**** Unmatched variable not free or fixed
     lambda(One,One)

**** Unmatched variable not free or fixed
     lambda(One,Two)

**** Unmatched variable not free or fixed
     lambda(One,Three)

**** Unmatched variable not free or fixed
     lambda(Two,One)

**** Unmatched variable not free or fixed
     lambda(Two,Two)

**** Unmatched variable not free or fixed
     lambda(Two,Three)

**** Unmatched variable not free or fixed
     lambda(Three,One)

**** Unmatched variable not free or fixed
     lambda(Three,Two)

**** Unmatched variable not free or fixed
     lambda(Three,Three)

**** Counts do not match
     Single equations in unmatched =E= blocks       18
     Unmatched single free variables                 0

**** Unmatched free variables = 0

**** Unmatched =E= equations = 18
     KKT(One,One)
     KKT(One,Two)
     KKT(One,Three)
     KKT(Two,One)
     KKT(Two,Two)
     KKT(Two,Three)
     KKT(Three,One)
     KKT(Three,Two)
     KKT(Three,Three)
     sl(One,One)
     sl(One,Two)
     sl(One,Three)
     sl(Two,One)
     sl(Two,Two)
     sl(Two,Three)
     sl(Three,One)
     sl(Three,Two)
     sl(Three,Three)
GAMS 24.7.4  r58773 Released Sep 19, 2016 WEX-WEI x86 64bit/MS Windows 05/04/18 14:52:16 Page 4
G e n e r a l   A l g e b r a i c   M o d e l i n g   S y s t e m
Model Statistics    SOLVE problem Using MCP From line 11


MODEL STATISTICS

BLOCKS OF EQUATIONS           2     SINGLE EQUATIONS           18
BLOCKS OF VARIABLES           3     SINGLE VARIABLES           27
NON ZERO ELEMENTS            36     NON LINEAR N-Z             18
DERIVATIVE POOL              20     CONSTANT POOL              19
CODE LENGTH                  64


GENERATION TIME      =        0.015 SECONDS      4 MB  24.7.4 r58773 WEX-WEI

**** SOLVE from line 11 ABORTED, EXECERROR = 28


EXECUTION TIME       =        0.015 SECONDS      4 MB  24.7.4 r58773 WEX-WEI


USER: GAMS Development Corporation, Washington, DC   G871201/0000CA-ANY
      Free Demo,  202-342-0180,  sales@gams.com,  www.gams.com   DC0000


**** FILE SUMMARY

Input      C:\Users\apfan\Documents\A (School)\General ISE\Research\KKT_research
           .gms
Output     C:\Users\apfan\Documents\gamsdir\projdir\KKT_research.lst

**** USER ERROR(S) ENCOUNTERED