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LEWISPOL.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME LEWISPOL
* Problem:
* ********
* Adrian Lewis Polynomial Problem,
* The problem is a transformation of a number theory integer
* programming problem.
* Source:
* A. Lewis, private communication.
* SIF input: A.R. Conn and Ph. Toint, March 1990.
* classification QOR2-AN-6-9
* Number of variables
IE N 6
* Problem parameters
IE DEG 3
* Penalty for integrality constraints
RE PEN 1.0D4
* Internal parameters
IE 0 0
IE 1 1
IE 2 2
IA DEG-1 DEG -1
IA N-1 N -1
IA N+1 N 1
VARIABLES
DO J 0 N-1
X A(J)
ND
GROUPS
* Objective function
N OBJ
* Constraints functions
DO J 0 N-1
AE C(0,J) 1.0
ZE D0 A(J) C(0,J)
ND
DO I 1 DEG-1
IA I-1 I -1
DO J I N-1
RI RJ J
A* C(I,J) C(I-1,J) RJ
ZE D(I) A(J) C(I,J)
ND
DO J 0 N-1
XE INT(J) A(J) -1.0
ZE INT(J) 'SCALE' PEN
ND
CONSTANTS
AE CT(0) -1.0
Z LEWIS D0 CT(0)
DO I 1 DEG-1
IA I-1 I -1
IM -I I -1
I+ N+1-I N+1 -I
RI VAL N+1-I
A* CT(I) CT(I-1) VAL
Z LEWIS D(I) CT(I)
ND
BOUNDS
XL LEWISPOL 'DEFAULT' -10.0
XU LEWISPOL 'DEFAULT' 10.0
START POINT
LEWISPOL A0 -1.0
LEWISPOL A1 1.0
LEWISPOL A2 1.0
LEWISPOL A3 0.0
LEWISPOL A4 1.0
LEWISPOL A5 -1.0
ELEMENT TYPE
EV SQ X
EV CB X
ELEMENT USES
DO J 0 N-1
XT O(J) SQ
ZV O(J) X A(J)
XT E(J) CB
ZV E(J) X A(J)
ND
GROUP USES
DO J 0 N-1
XE OBJ O(J)
XE INT(J) E(J)
ND
OBJECT BOUND
LO LEWISPOL 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS LEWISPOL
INDIVIDUALS
* Square
T SQ
F X * X
G X X + X
H X X 2.0
* Cube
T CB
F X**3
G X 3.0 * X**2
H X X 6.0 * X
ENDATA