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PENTAGON.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME PENTAGON
* Problem :
* *********
* An approximation to the problem of finding 3 points in a 2D
* pentagon whose minimal distance is maximal.
* Source:
* M.J.D. Powell,
* " TOLMIN: a Fortran package for linearly constrained
* optimization problems",
* Report DAMTP 1989/NA2, University of Cambridge, UK, 1989.
* SIF input: Ph. Toint, May 1990.
* classification OLR2-AY-6-15
* Constants
IE 0 0
IE 1 1
IE 3 3
IE 4 4
RE 2PI/5 1.2566371
* Computed parameters
DO J 0 4
RI RJ J
R* TJ 2PI/5 RJ
A( C(J) COS TJ
A( S(J) SIN TJ
ND
VARIABLES
DO I 1 3
X X(I)
X Y(I)
ND
GROUPS
N OBJ
DO I 1 3
DO J 0 4
ZL C(I,J) X(I) C(J)
ZL C(I,J) Y(I) S(J)
ND
CONSTANTS
X PENTAGON 'DEFAULT' 1.0
PENTAGON OBJ 0.0
BOUNDS
FR PENTAGON 'DEFAULT'
START POINT
PENTA X1 -1.0
PENTA Y1 0.0
PENTA X2 0.0
PENTA Y2 -1.0
PENTA X3 1.0
PENTA Y3 1.0
ELEMENT TYPE
EV IDIST XA YA
EV IDIST XB YB
IV IDIST DX DY
ELEMENT USES
T D12 IDIST
V D12 XA X1
V D12 YA Y1
V D12 XB X2
V D12 YB Y2
T D13 IDIST
V D13 XA X1
V D13 YA Y1
V D13 XB X3
V D13 YB Y3
T D32 IDIST
V D32 XA X3
V D32 YA Y3
V D32 XB X2
V D32 YB Y2
GROUP USES
E OBJ D12 D13
E OBJ D32
OBJECT BOUND
LO PENTAGON 0.0
* Solution
* LO SOLTN 1.36521631D-04
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS PENTAGON
TEMPORARIES
R D
R D9
R D10
INDIVIDUALS
T IDIST
R DX XA 1.0 XB -1.0
R DY YA 1.0 YB -1.0
A D DX * DX + DY * DY
A D9 D**9
A D10 D9 * D
F 1.0 / D**8
G DX -16.0 * DX / D9
G DY -16.0 * DY / D9
H DX DX 16.0 * ( 18.0 * DX * DX - D ) / D10
H DX DY 288.0 * DX * DY / D10
H DY DY 16.0 * ( 18.0 * DY * DY - D ) / D10
ENDATA