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HIMMELP4.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HIMMELP4
* Problem :
* *********
* A nonlinear problem with inequality constraints, attributed to Himmelblau
* by B.N. Pshenichnyj (case III)
* The problem is nonconvex and has redundant constraints at the solution.
* Source:
* B.N. Pshenichnyj
* "The Linearization Method for Constrained Optimization",
* Springer Verlag, SCM Series 22, Heidelberg, 1994
* SIF input: Ph. Toint, December 1994.
* classification OQR2-AN-2-3
* Problem data
RE B1 0.1963666677
RA B1 B1 75.0
RE B2 -.8112755343
RA B2 B2 -3.0
RE B6 -.8306567613
RA B6 B6 -6.0
RM -B2 B2 -1.0
RM -B6 B6 -1.0
VARIABLES
X1
X2
GROUPS
ZN OBJ X1 -B2
ZN OBJ X2 -B6
XG C5
XL C8 X2 -1.0
XL C9 X1 5.0 X2 100.0
CONSTANTS
Z HIMMELP4 OBJ B1
X HIMMELP4 C5 700.0
X HIMMELP4 C9 2775.0
BOUNDS
UP HIMMELP4 X1 75.0
UP HIMMELP4 X2 65.0
START POINT
XV HIMMELP4 X1 31.0
XV HIMMELP4 X2 48.0
* Solution
*XV HIMMELP4 X1 75.0
*XV HIMMELP4 X2 65.0
ELEMENT TYPE
EV OBNL X Y
EV 2PR X Y
EV SQ X
ELEMENT USES
T OB OBNL
ZV OB X X1
ZV OB Y X2
T X1X2 2PR
ZV X1X2 X X1
ZV X1X2 Y X2
T X1SQ SQ
ZV X1SQ X X1
T X2SQ SQ
ZV X2SQ X X2
GROUP USES
XE OBJ OB -1.0
XE C5 X1X2
XE C8 X1SQ 0.008
XE C9 X2SQ -1.0
OBJECT BOUND
* Solution
*LO SOLTN -59.01312394
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HIMMELP4
TEMPORARIES
R B3
R B4
R B5
R B7
R B8
R B9
R B10
R B11
R B12
R B13
R B14
R B15
R B16
R B17
R B18
R B19
R B20
R E
R DEDX
R DEDY
R D2EDXX
R D2EDXY
R D2EDYY
R A
R DADX
R D2ADXX
R B
R DBDX
R D2BDXX
R C
R DCDX
R D2CDXX
R F
R DFDY
R D2FDYY
R G
R DGDX
R D2GDXX
M EXP
INDIVIDUALS
T OBNL
A B3 .1269366345
A B4 -0.20567665
A B4 0.01 * B4
A B5 0.103450d-4
A B7 .0302344793
A B8 -0.12813448
A B8 0.01 * B8
A B9 0.352599d-4
A B10 -0.2266d-6
A B11 0.2564581253
A B12 -.003460403
A B13 0.135139d-4
A B14 -.1064434908
A B14 B14 - 28.0
A B15 -0.52375d-5
A B16 -0.63d-8
A B17 0.7d-9
A B18 0.3405462
A B18 0.001 * B18
A B19 -0.16638d-5
A B20 -2.86731123
A B20 B20-0.92d-8
A A B7*X+B8*X**2+B9*X**3+B10*X**4
A DADX B7+2.0*B8*X+3.0*B9*X**2+4.0*B10*X**3
A D2ADXX 2.0*B8+6.0*B9*X+12.0*B10*X**2
A B B18*X+B15*X**2+B16*X**3
A DBDX B18+2.0*B15*X+3.0*B16*X**2
A D2BDXX 2.0*B15+6.0*B16*X
A C B3*X**2+B4*X**3+B5*X**4
A DCDX 2.0*B3*X+3.0*B4*X**2+4.0*B5*X**3
A D2CDXX 2.0*B3+6.0*B4*X+12.0*B5*X**2
A F B11*Y**2+B12*Y**3+B13*Y**4
A DFDY 2.0*B11*Y+3.0*B12*Y**2+4.0*B13*Y**3
A D2FDYY 2.0*B11+ 6.0*B12*Y+12.0*B13*Y**2
A G B17*X**3+B19*X
A DGDX B19 + 3.0 * B17 * X**2
A D2GDXX 6.0 * B17 * X
A E EXP( 0.0005 * X * Y )
A DEDX 0.0005 * Y * E
A DEDY 0.0005 * X * E
A D2EDXX 0.0005 * Y * DEDX
A D2EDXY 0.0005 * ( Y * DEDY + E )
A D2EDYY 0.0005 * X * DEDY
F C + Y * A + F + B14 / ( 1.0 + Y )
F+ + B * Y**2 + G * Y**3 + B20 * E
G X DCDX + Y * DADX + DBDX * Y**2
G+ + DGDX * Y**3 + B20 * DEDX
G Y A + DFDY - B14 / ( 1.0 + Y )**2
G+ + 2.0 * B * Y + 3.0 * G * Y**2
G+ + B20 * DEDY
H X X D2CDXX + Y * D2ADXX + D2BDXX * Y**2
H+ + D2GDXX * Y**3 + B20 * D2EDXX
H X Y DADX + 2.0 * Y * DBDX
H+ + 3.0 * DGDX *Y**2 + B20 * D2EDXY
H Y Y D2FDYY + 2.0 * B14 / ( 1.0 + Y )**3
H+ + 2.0 * B + 6.0 * G * Y
H+ + B20 * D2EDYY
T 2PR
F X * Y
G X Y
G Y X
H X Y 1.0
T SQ
F X * X
G X X + X
H X X 2.0
ENDATA