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SCHMVETT.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME SCHMVETT
* Problem :
* *********
* The Schmidt and Vetters problem.
* This problem has N-2 trivial groups, all of which have 3 nonlinear
* elements
* Source:
* J.W. Schmidt and K. Vetters,
* "Albeitungsfreie Verfahren fur Nichtlineare Optimierungsproblem",
* Numerische Mathematik 15:263-282, 1970.
* See also Toint#35 and Buckley#14 (p90)
* SIF input: Ph. Toint, Dec 1989.
* classification OUR2-AY-V-0
* Number of variables
*IE N 3 $-PARAMETER original value
*IE N 10 $-PARAMETER
*IE N 100 $-PARAMETER
*IE N 500 $-PARAMETER
*IE N 1000 $-PARAMETER
IE N 5000 $-PARAMETER
*IE N 10000 $-PARAMETER
* Other parameters
IE 1 1
IA N-2 N -2
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 N-2
XN G(I)
ND
BOUNDS
FR SCHMVETT 'DEFAULT'
START POINT
XV SCHMVETT 'DEFAULT' 0.5
ELEMENT TYPE
EV SCH1 V1 V2
IV SCH1 U
EV SCH2 V1 V2
IV SCH2 U
EV SCH3 V1 V2
EV SCH3 V3
IV SCH3 U1 U2
ELEMENT USES
DO I 1 N-2
IA I+1 I 1
IA I+2 I 2
IA I+3 I 3
XT A(I) SCH1
ZV A(I) V1 X(I)
ZV A(I) V2 X(I+1)
XT B(I) SCH2
ZV B(I) V1 X(I+1)
ZV B(I) V2 X(I+2)
XT C(I) SCH3
ZV C(I) V1 X(I)
ZV C(I) V2 X(I+1)
ZV C(I) V3 X(I+2)
ND
GROUP USES
DO I 1 N-2
XE G(I) A(I) B(I)
XE G(I) C(I)
ND
OBJECT BOUND
* Solution
*LO SOLTN(3) -3.0
*LO SOLTN(10) -24.0
*LO SOLTN(100) -294.0
*LO SOLTN(500) -1494.0
*LO SOLTN(1000) -2994.0
*LO SOLTN(5000) ???
*LO SOLTN(10000) ???
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS SCHMVETT
TEMPORARIES
R T
R T2
R USQ
R HALFU
R SHALFU
R U2SQ
R A
R R
R E
R EXPE
R DEDA
R D2EDA2
R DAD1
R DAD2
R D2AD12
R D2AD22
R DEDASQ
R G
M SIN
M EXP
M COS
INDIVIDUALS
* Fraction element type
T SCH1
R U V1 1.0 V2 -1.0
A USQ U * U
A T 1.0 + USQ
A T2 T * T
F - 1.0 / T
G U 2.0 * U / T2
H U U 2.0 * ( 1.0 - 4.0 * USQ / T ) / T2
* Trigonometric element type
T SCH2
R U V1 3.14159265 V2 1.0
A HALFU 0.5 * U
A SHALFU SIN( HALFU )
F - SHALFU
G U - 0.5 * COS( HALFU )
H U U 0.25 * SHALFU
* Exponential element type
T SCH3
R U1 V1 1.0 V3 1.0
R U2 V2 1.0
A U2SQ U2 * U2
A A U1 / U2 - 2.0
A E - A * A
A EXPE EXP( E )
A DEDA - 2.0 * A
A D2EDA2 -2.0
A DAD1 1.0 / U2
A DAD2 - U1 / U2SQ
A D2AD12 - 1.0 / U2SQ
A D2AD22 2.0 * U1 / ( U2SQ * U2 )
A DEDASQ DEDA * DEDA
A G EXPE * DEDA
F - EXPE
G U1 - G * DAD1
G U2 - G * DAD2
H U1 U1 - EXPE * ( DEDASQ * DAD1 * DAD1
H+ + D2EDA2 * DAD1 * DAD1 )
H U1 U2 - EXPE * ( DEDASQ * DAD1 * DAD2
H+ + D2EDA2 * DAD1 * DAD2
H+ + DEDA * D2AD12 )
H U2 U2 - EXPE * ( DEDASQ * DAD2 * DAD2
H+ + D2EDA2 * DAD2 * DAD2
H+ + DEDA * D2AD22 )
ENDATA