Problem #2, MPL Code
TITLE
ENCE723_PB2
!Problem #2
!Formulation using MPL
!Note: use student version of conopt as solver
OPTION
ModelType = Nonlinear;
INDEX
DATA
VARIABLES
x1;
x2;
MACROS
MODEL
min x1;
SUBJECT TO
x1*x1 - 2*x1 + x2*x2 - 2*x2 + 2 <=1;
x1*x1 - 2*x1 + x2*x2 + 2*x2 + 2 <=1;
BOUNDS
FREE
BINARY
END
OUTPUT USING XPRESS-MP SOLVER
(solution is not correct, KKT conditions do not hold, this is a hard problem to solve)
MPL Modeling System - Copyright (c) 1988-2003, Maximal Software, Inc.
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MODEL STATISTICS
Problem name: ENCE723_PB2
Filename: ENCE723_PB2.mpl
Date: June 30, 2004
Time: 15:25
Parsing time: 0.00 sec
Solver: XPress
Objective value: 0.500000000000
Iterations: 0
Solution time: 0.00 sec
Result code: 1
Constraints: 2
Variables: 2
Nonzeros: 4
Density: 100 %
SOLUTION RESULT
Optimal solution found
MIN Z = 0.5000000000
DECISION VARIABLES
PLAIN VARIABLES
Variable Name Activity Reduced Cost
--------------------------------------------
x1 0.5000000000 0.0000000000
x2 0.0000000000 0.0000000000
--------------------------------------------
CONSTRAINTS
OUTPUT USING CONOPT (Solution is close)
MPL Modeling System - Copyright (c) 1988-2003, Maximal Software, Inc.
------------------------------------------------------------------------------
MODEL STATISTICS
Problem name: ENCE723_PB2
Filename: ENCE723_PB2.mpl
Date: June 30, 2004
Time: 15:27
Parsing time: 0.00 sec
Solver: Conopt
Objective value: 0.999989100072
Iterations: 15
Solution time: 0.03 sec
Result code: 201
Constraints: 2
Variables: 2
Nonzeros: 4
Density: 100 %
SOLUTION RESULT
Local optimum solution found
MIN Z = 0.9999891001
DECISION VARIABLES
PLAIN VARIABLES
Variable Name Activity Reduced Cost
------------------------------------------------------
x1 0.9999854668 0.0000000000
x2 0.0000000000 0.0000000000
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CONSTRAINTS
PLAIN CONSTRAINTS
Constraint Name Slack Shadow Price
------------------------------------------------------
c1 0.0000000000 0.0000000000
c2 0.0000000000 0.0000000000
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END
