bench 2 - BARON

VARIABLES             ff;
POSITIVE VARIABLES   a,b,c,d,e,f;
EQUATIONS     OBJ;
OBJ..  ff =E= a/(b+1E-15) + c/(d+1E-15) + e/(f+1E-15) + f/(a+1E-15) + 1E-7 * (a+b+c+d+e+f);

MODEL exactGlobalOpt /ALL/;
a.up = 1;
b.up = 1;
c.up = 1;
d.up = 1;
e.up = 1;
f.up = 1;

SOLVE exactGlobalOpt USING NLP MINIMIZING ff;



Output:

GAMS Rev 236  LEX-LEI 23.6.0 x86_64/Linux              03/26/11 06:27:58 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  VARIABLES             ff;
   2  POSITIVE VARIABLES   a,b,c,d,e,f;
   3  EQUATIONS     OBJ;
   4  OBJ..  ff =E= a/(b+1E-15) + c/(d+1E-15) + e/(f+1E-15) + f/(a+1E-15) + 1E-
      7 * (a+b+c+d+e+f);
   5
   6  MODEL exactGlobalOpt /ALL/;
   7  a.up = 1;
   8  b.up = 1;
   9  c.up = 1;
  10  d.up = 1;
  11  e.up = 1;
  12  f.up = 1;
  13
  14  SOLVE exactGlobalOpt USING NLP MINIMIZING ff;
  15
  16


COMPILATION TIME     =        0.000 SECONDS      2 Mb  LEX236-236 Nov  4, 2010
GAMS Rev 236  LEX-LEI 23.6.0 x86_64/Linux              03/26/11 06:27:58 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
Model Statistics    SOLVE exactGlobalOpt Using NLP From line 14


MODEL STATISTICS

BLOCKS OF EQUATIONS           1     SINGLE EQUATIONS            1
BLOCKS OF VARIABLES           7     SINGLE VARIABLES            7
NON ZERO ELEMENTS             7     NON LINEAR N-Z              6
DERIVATIVE POOL               6     CONSTANT POOL              18
CODE LENGTH                  41


GENERATION TIME      =        0.002 SECONDS      3 Mb  LEX236-236 Nov  4, 2010


EXECUTION TIME       =        0.002 SECONDS      3 Mb  LEX236-236 Nov  4, 2010
GAMS Rev 236  LEX-LEI 23.6.0 x86_64/Linux              03/26/11 06:27:58 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
Solution Report     SOLVE exactGlobalOpt Using NLP From line 14


               S O L V E      S U M M A R Y

     MODEL   exactGlobalOpt      OBJECTIVE  ff
     TYPE    NLP                 DIRECTION  MINIMIZE
     SOLVER  BARON               FROM LINE  14

**** SOLVER STATUS     3 Resource Interrupt
**** MODEL STATUS      2 Locally Optimal
**** OBJECTIVE VALUE                0.1076

 RESOURCE USAGE, LIMIT       1000.000      1000.000
 ITERATION COUNT, LIMIT         0    2000000000
 EVALUATION ERRORS              0             0

GAMS/BARON       BETA  6Nov10 23.6.0 LEX 21006.21007 LEI x86_64/Linux

Branch And Reduce Optimization Navigator
Nikolaos Sahinidis and Mohit Tawarmalani
The Optimization Firm, LLC.

  Total time elapsed:        000:16:40,    in seconds:       1000.00
       on parsing:           000:00:00,    in seconds:          0.00
       on preprocessing:     000:00:00,    in seconds:          0.00
       on navigating:        000:03:43,    in seconds:        222.64
       on relaxed:           000:09:24,    in seconds:        563.65
       on local:             000:02:07,    in seconds:        127.36
       on tightening:        000:01:08,    in seconds:         68.26
       on marginals:         000:00:05,    in seconds:          5.33
       on probing:           000:00:13,    in seconds:         12.74

  Total no. of BaR iterations:22845821
  Best solution found at node:    1132
  Max. no. of nodes in memory:  298702


===========================================================================
 BARON version 9.0.7. Built: LNX Mon Oct 4 13:04:39 EDT 2010

 Reference:
 Tawarmalani, M. and N. V. Sahinidis, A polyhedral
 branch-and-cut approach to global optimization,
 Mathematical Programming, 103(2), 225-249, 2005.

 BARON is a product of The Optimization Firm, LLC.
 Parts of the BARON software were created at the

Solution      = 0.107590878861  found at node 1132
Best possible = 9.8314889072E-10
Absolute gap  = 0.107590877877851  optca = 1E-9
Relative gap  = NA  optcr = 0.1


                       LOWER     LEVEL     UPPER    MARGINAL

---- EQU OBJ             .         .         .        1.000

                       LOWER     LEVEL     UPPER    MARGINAL

---- VAR ff             -INF      0.108     +INF       .
---- VAR a               .    1.6532E-6     1.000      .
---- VAR b               .    9.3892E-5     1.000      .
---- VAR c               .         .        1.000      .
---- VAR d               .    8.7623E-6     1.000      .
---- VAR e               .         .        1.000      .
---- VAR f               .    1.4876E-7     1.000      .


**** REPORT SUMMARY :        0     NONOPT
                             0 INFEASIBLE
                             0  UNBOUNDED
                             0     ERRORS


EXECUTION TIME       =        0.031 SECONDS      2 Mb  LEX236-236 Nov  4, 2010


USER: NEOS Server                                    G100907:1412AS-LNX
      University of Wisconsin-Madison                            DC8499
      License for teaching and research at degree granting institutions

**** ************* BETA release
**** GAMS Base Module BETA  6Nov10 23.6.0 LEX 21006.21007 LEI x86_64/Linux

**** ************* BETA release