GAMS Rev 138 MS Windows 10/29/06 08:33:05 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 * GAMS Solution to Kuhn-Tucker problems 2 * 28 October, 2006 3 COMPILATION TIME = 0.010 SECONDS 2.2 Mb WIN213-138 Feb 03, 2004 GAMS Rev 138 MS Windows 10/29/06 08:33:05 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 prob1 Using NLP From line 66 MODEL STATISTICS BLOCKS OF EQUATIONS 2 SINGLE EQUATIONS 2 BLOCKS OF VARIABLES 3 SINGLE VARIABLES 3 NON ZERO ELEMENTS 5 NON LINEAR N-Z 4 DERIVATIVE POOL 8 CONSTANT POOL 14 CODE LENGTH 27 GENERATION TIME = 0.040 SECONDS 2.9 Mb WIN213-138 Feb 03, 2004 EXECUTION TIME = 0.040 SECONDS 2.9 Mb WIN213-138 Feb 03, 2004 GAMS Rev 138 MS Windows 10/29/06 08:33:05 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 prob1 Using NLP From line 66 S O L V E S U M M A R Y MODEL prob1 OBJECTIVE F TYPE NLP DIRECTION MAXIMIZE SOLVER CONOPT FROM LINE 66 **** SOLVER STATUS 1 NORMAL COMPLETION **** MODEL STATUS 2 LOCALLY OPTIMAL **** OBJECTIVE VALUE -2.0000 RESOURCE USAGE, LIMIT 0.041 1000.000 ITERATION COUNT, LIMIT 12 10000 EVALUATION ERRORS 0 0 C O N O P T 3 MS Windows version 3.13C-015-050 Copyright (C) ARKI Consulting and Development A/S Bagsvaerdvej 246 A DK-2880 Bagsvaerd, Denmark Using default options. ** Optimal solution. Reduced gradient less than tolerance. CONOPT time Total 0.040 seconds of which: Function evaluations 0.000 = 0.0% 1st Derivative evaluations 0.000 = 0.0% Work length = 0.02 Mbytes Estimate = 0.02 Mbytes Max used = 0.01 Mbytes LOWER LEVEL UPPER MARGINAL ---- EQU obj1 . . . 1.000 ---- EQU cnst1 -INF -1.000 -1.000 2.000 obj1 objective function 1 cnst1 constraint 1 LOWER LEVEL UPPER MARGINAL ---- VAR x1 . 1.000 +INF . ---- VAR x2 . 1.000 +INF EPS ---- VAR F -INF -2.000 +INF . **** REPORT SUMMARY : 0 NONOPT 0 INFEASIBLE 0 UNBOUNDED 0 ERRORS GAMS Rev 138 MS Windows 10/29/06 08:33:05 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 prob2 Using NLP From line 74 MODEL STATISTICS BLOCKS OF EQUATIONS 3 SINGLE EQUATIONS 3 BLOCKS OF VARIABLES 3 SINGLE VARIABLES 3 NON ZERO ELEMENTS 6 NON LINEAR N-Z 2 DERIVATIVE POOL 8 CONSTANT POOL 14 CODE LENGTH 16 GENERATION TIME = 0.040 SECONDS 2.4 Mb WIN213-138 Feb 03, 2004 EXECUTION TIME = 0.050 SECONDS 2.4 Mb WIN213-138 Feb 03, 2004 GAMS Rev 138 MS Windows 10/29/06 08:33:05 Page 5 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 prob2 Using NLP From line 74 S O L V E S U M M A R Y MODEL prob2 OBJECTIVE F TYPE NLP DIRECTION MAXIMIZE SOLVER CONOPT FROM LINE 74 **** SOLVER STATUS 1 NORMAL COMPLETION **** MODEL STATUS 2 LOCALLY OPTIMAL **** OBJECTIVE VALUE -0.4000 RESOURCE USAGE, LIMIT 0.010 1000.000 ITERATION COUNT, LIMIT 7 10000 EVALUATION ERRORS 0 0 C O N O P T 3 MS Windows version 3.13C-015-050 Copyright (C) ARKI Consulting and Development A/S Bagsvaerdvej 246 A DK-2880 Bagsvaerd, Denmark Using default options. ** Optimal solution. There are no superbasic variables. CONOPT time Total 0.010 seconds of which: Function evaluations 0.000 = 0.0% 1st Derivative evaluations 0.000 = 0.0% Work length = 0.02 Mbytes Estimate = 0.02 Mbytes Max used = 0.01 Mbytes LOWER LEVEL UPPER MARGINAL ---- EQU obj1 . . . 1.000 ---- EQU cnst2 -INF -2.000 -2.000 0.400 ---- EQU cnst3 -INF -0.200 -0.200 EPS obj1 objective function 1 cnst2 constraint 2 cnst3 constraint 3 LOWER LEVEL UPPER MARGINAL ---- VAR x1 . 0.600 +INF . ---- VAR x2 . 0.200 +INF . ---- VAR F -INF -0.400 +INF . **** REPORT SUMMARY : 0 NONOPT 0 INFEASIBLE 0 UNBOUNDED 0 ERRORS GAMS Rev 138 MS Windows 10/29/06 08:33:05 Page 6 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 prob3 Using NLP From line 79 MODEL STATISTICS BLOCKS OF EQUATIONS 3 SINGLE EQUATIONS 3 BLOCKS OF VARIABLES 4 SINGLE VARIABLES 4 NON ZERO ELEMENTS 8 NON LINEAR N-Z 4 DERIVATIVE POOL 9 CONSTANT POOL 15 CODE LENGTH 36 GENERATION TIME = 0.050 SECONDS 2.4 Mb WIN213-138 Feb 03, 2004 EXECUTION TIME = 0.050 SECONDS 2.4 Mb WIN213-138 Feb 03, 2004 GAMS Rev 138 MS Windows 10/29/06 08:33:05 Page 7 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 prob3 Using NLP From line 79 S O L V E S U M M A R Y MODEL prob3 OBJECTIVE F TYPE NLP DIRECTION MAXIMIZE SOLVER CONOPT FROM LINE 79 **** SOLVER STATUS 1 NORMAL COMPLETION **** MODEL STATUS 2 LOCALLY OPTIMAL **** OBJECTIVE VALUE -3.5556 RESOURCE USAGE, LIMIT 0.010 1000.000 ITERATION COUNT, LIMIT 6 10000 EVALUATION ERRORS 0 0 C O N O P T 3 MS Windows version 3.13C-015-050 Copyright (C) ARKI Consulting and Development A/S Bagsvaerdvej 246 A DK-2880 Bagsvaerd, Denmark Using default options. ** Optimal solution. Reduced gradient less than tolerance. CONOPT time Total 0.010 seconds of which: Function evaluations 0.000 = 0.0% 1st Derivative evaluations 0.000 = 0.0% Work length = 0.02 Mbytes Estimate = 0.02 Mbytes Max used = 0.01 Mbytes LOWER LEVEL UPPER MARGINAL ---- EQU obj2 . . . 1.000 ---- EQU cnst4 . . . 3.528 ---- EQU cnst5 -INF -2.000 -2.000 1.778 obj2 objective function 2 cnst4 constraint 4 cnst5 constraint 5 LOWER LEVEL UPPER MARGINAL ---- VAR x1 . 0.778 +INF . ---- VAR x2 . 0.444 +INF EPS ---- VAR x3 -INF 1.764 +INF . ---- VAR F -INF -3.556 +INF . **** REPORT SUMMARY : 0 NONOPT 0 INFEASIBLE 0 UNBOUNDED 0 ERRORS GAMS Rev 138 MS Windows 10/29/06 08:33:05 Page 8 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 prob4 Using LP From line 85 MODEL STATISTICS BLOCKS OF EQUATIONS 3 SINGLE EQUATIONS 3 BLOCKS OF VARIABLES 3 SINGLE VARIABLES 3 NON ZERO ELEMENTS 7 GENERATION TIME = 0.060 SECONDS 2.4 Mb WIN213-138 Feb 03, 2004 EXECUTION TIME = 0.060 SECONDS 2.4 Mb WIN213-138 Feb 03, 2004 GAMS Rev 138 MS Windows 10/29/06 08:33:05 Page 9 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 prob4 Using LP From line 85 S O L V E S U M M A R Y MODEL prob4 OBJECTIVE F TYPE LP DIRECTION MAXIMIZE SOLVER CPLEX FROM LINE 85 **** SOLVER STATUS 1 NORMAL COMPLETION **** MODEL STATUS 1 OPTIMAL **** OBJECTIVE VALUE 2.0000 RESOURCE USAGE, LIMIT 0.010 1000.000 ITERATION COUNT, LIMIT 0 10000 GAMS/Cplex Jan 19, 2004 WIN.CP.CP 21.3 025.027.041.VIS For Cplex 9.0 Cplex 9.0.0, GAMS Link 25 Optimal solution found. Objective : 2.000000 LOWER LEVEL UPPER MARGINAL ---- EQU obj3 . . . 1.000 ---- EQU cnst6 -INF 2.000 2.000 . ---- EQU cnst7 -INF 1.000 1.000 2.000 obj3 objective function 3 cnst6 constraint 6 cnst7 constraint 7 LOWER LEVEL UPPER MARGINAL ---- VAR x1 . . +INF -1.000 ---- VAR x2 . 1.000 +INF . ---- VAR F -INF 2.000 +INF . **** REPORT SUMMARY : 0 NONOPT 0 INFEASIBLE 0 UNBOUNDED GAMS Rev 138 MS Windows 10/29/06 08:33:05 Page 10 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 prob5 Using MIP From line 90 MODEL STATISTICS BLOCKS OF EQUATIONS 3 SINGLE EQUATIONS 3 BLOCKS OF VARIABLES 3 SINGLE VARIABLES 3 NON ZERO ELEMENTS 7 DISCRETE VARIABLES 2 GENERATION TIME = 0.040 SECONDS 2.4 Mb WIN213-138 Feb 03, 2004 EXECUTION TIME = 0.050 SECONDS 2.4 Mb WIN213-138 Feb 03, 2004 GAMS Rev 138 MS Windows 10/29/06 08:33:05 Page 11 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 prob5 Using MIP From line 90 S O L V E S U M M A R Y MODEL prob5 OBJECTIVE F TYPE MIP DIRECTION MAXIMIZE SOLVER CPLEX FROM LINE 90 **** SOLVER STATUS 1 NORMAL COMPLETION **** MODEL STATUS 1 OPTIMAL **** OBJECTIVE VALUE 9.0000 RESOURCE USAGE, LIMIT 0.020 1000.000 ITERATION COUNT, LIMIT 0 10000 GAMS/Cplex Jan 19, 2004 WIN.CP.CP 21.3 025.027.041.VIS For Cplex 9.0 Cplex 9.0.0, GAMS Link 25 Proven optimal solution. MIP Solution: 9.000000 (0 iterations, 0 nodes) Final Solve: 9.000000 (0 iterations) Best possible: 9.000000 Absolute gap: 0.000000 Relative gap: 0.000000 LOWER LEVEL UPPER MARGINAL ---- EQU obj4 . . . 1.000 ---- EQU cnst8 -INF -3.000 . . ---- EQU cnst9 -INF 3.000 3.500 . obj4 objective function 4 cnst8 constraint 8 cnst9 constraint 9 LOWER LEVEL UPPER MARGINAL ---- VAR x4 . 3.000 100.000 3.000 ---- VAR x5 . . 100.000 -7.000 ---- VAR F -INF 9.000 +INF . **** REPORT SUMMARY : 0 NONOPT 0 INFEASIBLE 0 UNBOUNDED GAMS Rev 138 MS Windows 10/29/06 08:33:05 Page 12 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 E x e c u t i o n **** REPORT FILE SUMMARY results C:\DennisMcL\MIT_classes\MIT1731_06\www\Probsets\PS06\PS2\PS06_2.res EXECUTION TIME = 0.030 SECONDS 2.4 Mb WIN213-138 Feb 03, 2004 USER: Civil & Environmental Engineering G040407:1247AP-WIN MIT DC3218 License for teaching and research at degree granting institutions **** FILE SUMMARY INPUT C:\DennisMcL\MIT_classes\MIT1731_06\www\Probsets\PS06\PS2\PS06_2.gms OUTPUT C:\DennisMcL\MIT_classes\MIT1731_06\www\Probsets\PS06\PS2\PS06_2.lst