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OBSTCLBL.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME OBSTCLBL
* Problem :
* *********
* A quadratic obstacle problem by Dembo and Tulowitzki
* The problem comes from the obstacle problem on a rectangle.
* The rectangle is discretized into (px-1)(py-1) little rectangles. The
* heights of the considered surface above the corners of these little
* rectangles are the problem variables, There are px*py of them.
* Source:
* R. Dembo and U. Tulowitzki,
* "On the minimization of quadratic functions subject to box
* constraints",
* WP 71, Yale University (new Haven, USA), 1983.
* See also More 1989 (Problem B, Starting point L)
* SIF input: Ph. Toint, Dec 1989.
* classification QBR2-AY-V-0
* PX is the number of points along the X side of the rectangle
* PY is the number of points along the Y side of the rectangle
*IE PX 4 $-PARAMETER n = 16
*IE PY 4 $-PARAMETER
*IE PX 10 $-PARAMETER n = 100 original value
*IE PY 10 $-PARAMETER original value
*IE PX 23 $-PARAMETER n = 529
*IE PY 23 $-PARAMETER
*IE PX 32 $-PARAMETER n = 1024
*IE PY 32 $-PARAMETER
*IE PX 75 $-PARAMETER n = 5625
*IE PY 75 $-PARAMETER
IE PX 100 $-PARAMETER n = 10000
IE PY 100 $-PARAMETER
*IE PX 125 $-PARAMETER n = 15625
*IE PY 125 $-PARAMETER
* The force constant
RE C 1.0 $-PARAMETER the force constant
* Define the stepsize in the X direction and its inverse
IA PX-1 PX -1
RI RPX-1 PX-1
RD HX RPX-1 1.0
RD 1/HX HX 1.0
* Define the stepsize in the Y direction and its inverse
IA PY-1 PY -1
RI RPY-1 PY-1
RD HY RPY-1 1.0
RD 1/HY HY 1.0
* Define a few helpful parameters
R* HXHY HX HY
R* HX/HY HX 1/HY
R* HY/HX HY 1/HX
RM HY/4HX HY/HX 0.25
RM HX/4HY HX/HY 0.25
R* C0 HXHY C
RM LC C0 -1.0
IE 1 1
IE 2 2
VARIABLES
* Define one variable per discretized point in the unit square
DO J 1 PX
DO I 1 PY
X X(I,J)
ND
GROUPS
* Define a group per interior node
DO I 2 PY-1
DO J 2 PX-1
ZN G(I,J) X(I,J) LC
ND
BOUNDS
* Fix the variables on the lower and upper edges of the unit square
DO J 1 PX
XX OBSTCLBL X(1,J) 0.0
XX OBSTCLBL X(PY,J) 0.0
ND
* Fix the variables on the left and right edges of the unit square
DO I 2 PY-1
XX OBSTCLBL X(I,PX) 0.0
XX OBSTCLBL X(I,1) 0.0
ND
* Describe the lower obstacle (problem B)
DO I 2 PY-1
IA I-1 I -1
RI RI-1 I-1
R* XI1 RI-1 HY
RM 3XI1 XI1 9.2
R( SXI1 SIN 3XI1
DO J 2 PX-1
IA J-1 J -1
RI RJ-1 J-1
R* XI2 RJ-1 HX
RM 3XI2 XI2 9.3
R( SXI2 SIN 3XI2
R* L1 SXI1 SXI2
R* L2 L1 L1
R* LOW L2 L1
ZL OBSTCLBL X(I,J) LOW
ND
* Describe the upper obstacle (problem B)
DO I 2 PY-1
IA I-1 I -1
RI RI-1 I-1
R* XI1 RI-1 HY
RM 3XI1 XI1 9.2
R( SXI1 SIN 3XI1
DO J 2 PX-1
IA J-1 J -1
RI RJ-1 J-1
R* XI2 RJ-1 HX
RM 3XI2 XI2 9.3
R( SXI2 SIN 3XI2
R* L1 SXI1 SXI2
R* L2 L1 L1
RA UPP L2 0.02
ZU OBSTCLBL X(I,J) UPP
ND
START POINT
* Start from the boundary values on the lower and upper edges
DO J 1 PX
X OBSTCLBL X(1,J) 0.0
X OBSTCLBL X(PY,J) 0.0
ND
* Start from the boundary values on the left and right edges
DO I 2 PY-1
X OBSTCLBL X(I,PX) 0.0
X OBSTCLBL X(I,1) 0.0
ND
* Describe the lower obstacle (starting point L)
DO I 2 PY-1
IA I-1 I -1
RI RI-1 I-1
R* XI1 RI-1 HY
RM 3XI1 XI1 9.2
R( SXI1 SIN 3XI1
DO J 2 PX-1
IA J-1 J -1
RI RJ-1 J-1
R* XI2 RJ-1 HX
RM 3XI2 XI2 9.3
R( SXI2 SIN 3XI2
R* L1 SXI1 SXI2
R* L2 L1 L1
R* LOW L2 L1
Z OBSTCLBL X(I,J) LOW
ND
ELEMENT TYPE
EV ISQ V1 V2
IV ISQ U
ELEMENT USES
* Each node has four elements
DO I 2 PY-1
IA I-1 I -1
IA I+1 I 1
DO J 2 PX-1
IA J-1 J -1
IA J+1 J 1
XT A(I,J) ISQ
ZV A(I,J) V1 X(I+1,J)
ZV A(I,J) V2 X(I,J)
XT B(I,J) ISQ
ZV B(I,J) V1 X(I,J+1)
ZV B(I,J) V2 X(I,J)
XT C(I,J) ISQ
ZV C(I,J) V1 X(I-1,J)
ZV C(I,J) V2 X(I,J)
XT D(I,J) ISQ
ZV D(I,J) V1 X(I,J-1)
ZV D(I,J) V2 X(I,J)
ND
GROUP USES
DO I 2 PY-1
DO J 2 PX-1
ZE G(I,J) A(I,J) HY/4HX
ZE G(I,J) B(I,J) HX/4HY
ZE G(I,J) C(I,J) HY/4HX
ZE G(I,J) D(I,J) HX/4HY
ND
OBJECT BOUND
* Solution
*LO SOLTN(4) -0.0081108
*LO SOLTN(10) 2.87503823
*LO SOLTN(23) 6.51932527
*LO SOLTN(32) 6.88708670
*LO SOLTN(75) ???
*LO SOLTN(100) ???
*LO SOLTN(125) ???
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS OBSTCLBL
INDIVIDUALS
* Difference squared
T ISQ
R U V1 1.0 V2 -1.0
F U * U
G U U + U
H U U 2.0
ENDATA