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HIMMELBK.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HIMMELBK
* Problem :
* *********
* A blending problem for multi-component mixtures, by Paviani.
* It has a linear objective and linear and nonlinear constraints.
* Compared to the problem specified in Himmelblau, the inequality
* constraints have been removed, because, as stated in this source,
* they impose that
* X(1)=X(2)=X(3)=X(7)=X(9)=X(9)=X(13)=X(14)=X(15)=X(19)=X(20)=X(21)=0
* which is clearly contradictory with the given solution(s). As
* there does not seem to be a natural way to correct this statement
* without knowing more about the original problem, the troublesome
* constraints have been removed.
* Source: from problem 20 in
* D.H. Himmelblau,
* "Applied nonlinear programming",
* McGraw-Hill, New-York, 1972.
* SIF input: Ph. Toint, March 1991.
* classification LOR2-MN-24-14
* Problem data
RE F 142.22471 $ F = 0.70302 * 530 * 14.7 / 40.0
RE B1 44.094
RE B2 58.12
RE B3 58.12
RE B4 137.4
RE B5 120.9
RE B6 170.9
RE B7 62.501
RE B8 84.94
RE B9 133.425
RE B10 82.507
RE B11 46.07
RE B12 60.097
RE B13 44.094
RE B14 58.12
RE B15 58.12
RE B16 137.4
RE B17 120.9
RE B18 170.9
RE B19 62.501
RE B20 84.94
RE B21 133.425
RE B22 82.507
RE B23 46.07
RE B24 60.097
RE C1 123.7
RE C2 31.7
RE C3 45.7
RE C4 14.7
RE C5 84.7
RE C6 27.7
RE C7 49.7
RE C8 7.1
RE C9 2.1
RE C10 17.7
RE C11 0.85
RE C12 0.64
RE D1 123.7
RE D2 31.7
RE D3 45.7
RE D4 14.7
RE D5 84.7
RE D6 27.7
RE D7 49.7
RE D8 7.1
RE D9 2.1
RE D10 17.7
RE D11 0.85
RE D12 0.64
* Constants
IE 1 1
IE 12 12
IE 13 13
IE 24 24
VARIABLES
DO K 1 24
X X(K)
ND
GROUPS
N OBJ X1 0.0693 X2 0.0577
N OBJ X3 0.05 X4 0.2
N OBJ X5 0.26 X6 0.55
N OBJ X7 0.06 X8 0.1
N OBJ X9 0.12 X10 0.18
N OBJ X11 0.1 X12 0.09
N OBJ X13 0.0693 X14 0.0577
N OBJ X15 0.05 X16 0.2
N OBJ X17 0.26 X18 0.55
N OBJ X19 0.06 X20 0.1
N OBJ X21 0.12 X22 0.18
N OBJ X23 0.1 X24 0.09
DO I 1 12
XE CA(I)
ND
DO I 1 24
XE CA13 X(I) 1.0
ND
DO I 1 12
IA I+12 I 12
AD 1/DI D(I) 1.0
ZE CA14 X(I) 1/DI
A/ F/BI+12 F B(I+12)
ZE CA14 X(I+12) F/BI+12
ND
CONSTANTS
X HIMMELBK CA13 1.0
X HIMMELBK CA14 1.671
START POINT
XV HIMMELBK 'DEFAULT' 0.04
ELEMENT TYPE
EV 2PR X Y
ELEMENT USES
DO I 1 12
IA I+12 I 12
DO J 1 12
XT E(I,J) 2PR
ZV E(I,J) X X(I+12)
ZV E(I,J) Y X(J)
OD J
DO J 13 24
XT E(I,J) 2PR
ZV E(I,J) X X(I)
ZV E(I,J) Y X(J)
OD J
OD I
GROUP USES
DO I 1 12
IA I+12 I 12
DO J 1 12
A/ BI/BJ B(I) B(J)
RM 40BI/BJ BI/BJ 40.0
ZE CA(I) E(I,J) 40BI/BJ
OD J
DO J 13 24
A/ B+/BJ B(I+12) B(J)
A* CB+/BJ C(I) B+/BJ
RM -CB+/BJ CB+/BJ -1.0
ZE CA(I) E(I,J) -CB+/BJ
OD J
OD I
OBJECT BOUND
* Solution
*LO SOLTN 0.0893344
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HIMMELBK
INDIVIDUALS
T 2PR
F X * Y
G X Y
G Y X
H X Y 1.0
ENDATA