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GRIDNETH.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME GRIDNETH
* Problem :
* *********
* The nonlinear network problem by Toint and Tuyttens,
* Source:
* Ph.L. Toint and D. Tuyttens,
* "On large scale nonlinear network optimization",
* Mathematical Programming B, vol. 48(1), pp.125-159, 1990.
* This version has 60 variables and has bounds corresponding
* to i = 0 and a = 1 and r = 0.1.
* The number of variables is N = 2*NS*(NS-1), where NS = 2*L+2.
* SIF input: Ph. Toint, May 1990.
* minor correction by Ph. Shott, Jan 1995.
* classification ONR2-AY-V-V
* Problem parameters
*IE L 2 $-PARAMETER number of vert/horiz. cycles
*IE L 10 $-PARAMETER number of vert/horiz. cycles
*IE L 20 $-PARAMETER number of vert/horiz. cycles
IE L 30 $-PARAMETER number of vert/horiz. cycles
*IE L 40 $-PARAMETER number of vert/horiz. cycles
RE C 2.0 $-PARAMETER log of condition number
RE R 0.1 $-PARAMETER bound parameter
RE A 1.0 $-PARAMETER amount of non-quadraticity
* Constants
IE 1 1
IE 2 2
IE 3 3
IE 4 4
RE LN10 2.302585093
* Computed parameters
IA L-1 L -1
IM 2L L 2
IA NS 2L 2
IA NS-1 NS -1
IM 2NS NS 2
IA P 2NS -1
IM 2P P 2
IM -P P -1
IA P-1 P -1
IA P-2 P -2
RI RL-1 L-1
RD 1/L-1 RL-1 1.0
R* CLN10 LN10 C
R* BETA CLN10 1/L-1
RM A/100 A 0.01
RM SMALLA A/100 0.0008333333333
VARIABLES
* Define two variables per node in the grid.
* The first corresponds to flow from the current node to the
* node on the right; the second corresponds to that to the node
* above.
IE N 0
DO I 1 NS-1
DO J 1 NS-1
IA N N 1
X X(N) $ flow to the right
IA N N 1
X X(N) $ flow to above
OD J
IA N N 1
X X(N) $ flow to above
ND
DO J 1 NS-1
IA N N 1
X X(N) $ flow to the right
ND
IA N-1 N -1
GROUPS
* Objective is nonlinear
N OBJ
* Network constraints for the bottom row
XE C(1,1) X(1) 1.0 X(2) 1.0
IE K 2
DO J 2 NS-1
IA K K 2
IA K-1 K -1
IA K-3 K -3
XE C(1,J) X(K-1) 1.0 X(K) 1.0
XE C(1,J) X(K-3) -1.0
OD J
IA K K 1
IA K-2 K -2
XE C(1,NS) X(K) 1.0
XE C(1,NS) X(K-2) -1.0
* Network constraints for the middle rows
DO I 2 NS-1
IA K K 2
IA K-1 K -1
I+ K-P K -P
XE C(I,1) X(K-1) 1.0 X(K) 1.0
XE C(I,1) X(K-P) -1.0
DO J 2 NS-1
IA K K 2
IA K-1 K -1
IA K-3 K -3
I+ K-P K -P
XE C(I,J) X(K-1) 1.0 X(K) 1.0
XE C(I,J) X(K-3) -1.0 X(K-P) -1.0
OD J
IA K K 1
IA K-2 K -2
I+ K-P K -P
XE C(I,NS) X(K) 1.0
XE C(I,NS) X(K-2) -1.0 X(K-P) -1.0
ND
* Network constraints for the top row
IA K K 1
IA K-1 K -1
IA -Q -P 1
I+ TW K -Q
XE C(NS,1) X(K) 1.0
XE C(NS,1) X(TW) -1.0
DO J 2 NS-1
IA K K 1
IA K-1 K -1
IA -Q -Q 1
I+ K-Q K -Q
XE C(NS,J) X(K) 1.0
XE C(NS,J) X(K-1) -1.0 X(K-Q) -1.0
ND
IA K K 1
IA K-1 K -1
I+ TE K -Q
XE C(NS,NS) X(K-1) -1.0 X(TE) -1.0
CONSTANTS
X GRIDNETH C(1,1) 10.0
X GRIDNETH C(NS,NS) -10.0
BOUNDS
FR GRIDNETH 'DEFAULT'
START POINT
XV GRIDNETH 'DEFAULT' 0.0
ELEMENT TYPE
EV SQ X
EV SQR X Y
EV DENSE V1 V2
EV DENSE V3 V4
EV DENSE V5 V6
EV DENSE V7 V8
EV DENSE V9 V10
EV DENSE V11 V12
EV DENSE V13 V14
EV DENSE V15 V16
EV DENSE V17 V18
EV DENSE V19 V20
EV DENSE V21 V22
EV DENSE V23 V24
EV DENSE V25 V26
EV DENSE V27 V28
EV DENSE V29 V30
EV DENSE V31 V32
EV DENSE V33 V34
EV DENSE V35 V36
EV DENSE V37 V38
EV DENSE V39 V40
EV DENSE V41 V42
EV DENSE V43 V44
EV DENSE V45 V46
EV DENSE V47 V48
EV DENSE V49 V50
EV DENSE V51 V52
EV DENSE V53 V54
EV DENSE V55 V56
EV DENSE V57 V58
EV DENSE V59 V60
IV DENSE U
ELEMENT USES
DO K 1 N
XT E(K) SQ
ZV E(K) X X(K)
ND
DO K 1 N-1
IA K+1 K 1
XT B(K) SQR
ZV B(K) X X(K)
ZV B(K) Y X(K+1)
ND
T BIG DENSE
V BIG V1 X1
V BIG V2 X2
V BIG V3 X3
V BIG V4 X4
V BIG V5 X5
V BIG V6 X6
V BIG V7 X7
V BIG V8 X8
V BIG V9 X9
V BIG V10 X10
V BIG V11 X11
V BIG V12 X12
V BIG V13 X13
V BIG V14 X14
V BIG V15 X15
V BIG V16 X16
V BIG V17 X17
V BIG V18 X18
V BIG V19 X19
V BIG V20 X20
V BIG V21 X21
V BIG V22 X22
V BIG V23 X23
V BIG V24 X24
V BIG V25 X25
V BIG V26 X26
V BIG V27 X27
V BIG V28 X28
V BIG V29 X29
V BIG V30 X30
V BIG V31 X31
V BIG V32 X32
V BIG V33 X33
V BIG V34 X34
V BIG V35 X35
V BIG V36 X36
V BIG V37 X37
V BIG V38 X38
V BIG V39 X39
V BIG V40 X40
V BIG V41 X41
V BIG V42 X42
V BIG V43 X43
V BIG V44 X44
V BIG V45 X45
V BIG V46 X46
V BIG V47 X47
V BIG V48 X48
V BIG V49 X49
V BIG V50 X50
V BIG V51 X51
V BIG V52 X52
V BIG V53 X53
V BIG V54 X54
V BIG V55 X55
V BIG V56 X56
V BIG V57 X57
V BIG V58 X58
V BIG V59 X59
V BIG V60 X60
GROUP USES
* Bottom row outside the cycles
DO J 1 P-2
DI J 4
XE OBJ E(J) 0.01
ND
* Side rows outside the cycles
DO IW 2 TW
DI IW 2P
I+ IE IW P-2
XE OBJ E(IE) 0.01 E(IW) 0.01
ND
* Top row outside the cycles
I+ HTW TW P-1
DO J HTW N
DI J 2
XE OBJ E(J) 0.01
ND
* Cycles
DO JK 1 L
* Compute the cycle coefficient
IA JK-1 JK -1
RI RJK-1 JK-1
R* EX RJK-1 BETA
R( AK EXP EX
RM AS AK 0.01
* Set starting arcs for the vertical and horizontal cycles
IM VW JK 4
IA IW VW 0
IM 2JK JK 2
IA 2JK-1 2JK -1
I* P2JK-1 2JK-1 P
IA HB P2JK-1 1
IA IB HB 0
* Loop on the long sides of both cycles
DO K 1 NS-1
* West side of the JKth vertical cycle
ZE OBJ E(IW) AS
* East side of the JKth vertical cycle
IA IE IW 2
ZE OBJ E(IE) AS
* Bottom side of the JKth horizontal cycle
ZE OBJ E(IB) AS
* Top side of the JKth horizontal cycle
I+ IT IB P
ZE OBJ E(IT) AS
* Increment
I+ IW IW P
IA IB IB 2
* End the loop on the long sides
OD K
* Bottom side of the JKth vertical cycle
IA VW-1 VW -1
ZE OBJ E(VW-1) AS
* Top side of the JKth vertical cycle
IA TE HTW -1
I+ TS TE 2JK
ZE OBJ E(TS) AS
* West side of the JKth horizontal cycle
IA KW HB 1
ZE OBJ E(KW) AS
* East side of the JKth horizontal cycle
I+ KE P2JK-1 P
ZE OBJ E(KE) AS
ND
* Non quadratic terms
DO K 1 N-1
ZE OBJ B(K) A/100
ND
* Dense term
ZE OBJ BIG SMALLA
OBJECT BOUND
LO GRIDNETH 0.0
* Solution
*LO SOLTN 39.609245
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS GRIDNETH
TEMPORARIES
R A
R SQRA
R ASQRA
R ISQRA
R B
R C
R TENPU
M SQRT
INDIVIDUALS
T SQ
F X * X
G X X + X
H X X 2.0
T SQR
A A 1.0 + 2.0 * X * ( X - Y) + Y * Y
A SQRA SQRT( A )
A ASQRA A * SQRA
A ISQRA 1.0 / SQRA
A B X + X - Y
A C Y - X
F SQRA
G X B / SQRA
G Y C / SQRA
H X X - B * B / ASQRA + ISQRA + ISQRA
H X Y - B * C / ASQRA - ISQRA
H Y Y - C * C / ASQRA + ISQRA
T DENSE
R U V1 -1.0 V2 1.0
R U V3 -1.0 V4 1.0
R U V5 -1.0 V6 1.0
R U V7 -1.0 V8 1.0
R U V9 -1.0 V10 1.0
R U V11 -1.0 V12 1.0
R U V13 -1.0 V14 1.0
R U V15 -1.0 V16 1.0
R U V17 -1.0 V18 1.0
R U V19 -1.0 V20 1.0
R U V21 -1.0 V22 1.0
R U V23 -1.0 V24 1.0
R U V25 -1.0 V26 1.0
R U V27 -1.0 V28 1.0
R U V29 -1.0 V30 1.0
R U V31 -1.0 V32 1.0
R U V33 -1.0 V34 1.0
R U V35 -1.0 V36 1.0
R U V37 -1.0 V38 1.0
R U V39 -1.0 V40 1.0
R U V41 -1.0 V42 1.0
R U V43 -1.0 V44 1.0
R U V45 -1.0 V46 1.0
R U V47 -1.0 V48 1.0
R U V49 -1.0 V50 1.0
R U V51 -1.0 V52 1.0
R U V53 -1.0 V54 1.0
R U V55 -1.0 V56 1.0
R U V57 -1.0 V58 1.0
R U V59 -1.0 V60 1.0
A TENPU 10.0 + U
F TENPU**4
G U 4.0 * TENPU**3
H U U 12.0 * TENPU**2
ENDATA