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GRIDNETF.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME GRIDNETF
* Problem :
* *********
* A nonlinear network problem on a square grid,
* 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: bounds corresponding to i = 1 and a = 1 and r = 0.1.
* NOTE THAT THE DENSE TERM IS OMITTED FROM THE OBJECTIVE, the
* Hessian being tridiagonal.
* The number of variables is N = 2*NS*(NS-1), where NS = 2*L+2.
* SIF input: Ph. Toint, March 1990.
* classification ONR2-AN-V-V
* Problem parameters: number of horizontal and vertical cycles
*IE L 2 $-PARAMETER n = 60 original value
*IE L 4 $-PARAMETER n = 180
*IE L 8 $-PARAMETER n = 612
*IE L 10 $-PARAMETER n = 924
*IE L 20 $-PARAMETER n = 3444
IE L 30 $-PARAMETER n = 7564
*IE L 40 $-PARAMETER n = 13284
* Other problem parameters
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
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
OD I
* 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
OD J
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 GRIDNETF C(1,1) 10.0
X GRIDNETF C(NS,NS) -10.0
BOUNDS
FR GRIDNETF 'DEFAULT'
* Lower bound for the MOD3 arcs
DO I 3 N
DI I 3
ZL GRIDNETF X(I) R
ND
START POINT
XV GRIDNETF 'DEFAULT' 0.0
ELEMENT TYPE
EV SQ X
EV SQR X Y
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
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
OBJECT BOUND
LO GRIDNETF 0.0
* Solution
*LO SOLTN(2) 4.0213D+01
*LO SOLTN(4) 5.1648D+01
*LO SOLTN(8) 7.6079D+01
*LO SOLTN(10) 8.7860D+01
*LO SOLTN(20) 1.4525D+02
*LO SOLTN(30)
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS GRIDNETF
TEMPORARIES
R A
R SQRA
R ASQRA
R ISQRA
R B
R C
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
ENDATA