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FLETCHER.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME FLETCHER
* Problem :
* *********
* A problem found in Fletcher's book. The problem is to find the least area
* of a right-angled triangle which contains a circle of unit radius.
* Source:
* R. Fletcher
* "Practical Methods of Optimization",
* second edition, Wiley, 1987.
* SIF input: Ph. Toint, March 1994.
* classification QOR2-AN-4-4
VARIABLES
X1
X2
X3
X4
GROUPS
* Objective function
XN OBJ
* Constraints
XE C1
XG C2 X1 1.0 X3 -1.0
XG C3 X2 1.0 X4 -1.0
XG C4 X3 1.0 X4 -1.0
CONSTANTS
FLETCHER C1 -1.0
FLETCHER C2 1.0
FLETCHER C3 1.0
BOUNDS
FR FLETCHER 'DEFAULT'
LO FLETCHER X4 1.0
START POINT
XV FLETCHER 'DEFAULT' 1.0
ELEMENT TYPE
EV 2PR XX YY
EV SQ XX
EV SPEC XX YY
EV SPEC VV WW
ELEMENT USES
XT OBE1 2PR
ZV OBE1 XX X1
ZV OBE1 YY X2
XT C1E1 SPEC
ZV C1E1 XX X1
ZV C1E1 YY X2
ZV C1E1 VV X3
ZV C1E1 WW X4
XT X3SQ SQ
ZV X3SQ XX X3
XT X4SQ SQ
ZV X4SQ XX X4
GROUP USES
XE OBJ OBE1
XE C1 C1E1
XE C1 X3SQ -1.0 X4SQ -1.0
OBJECT BOUND
* Solution
*LO SOLTN
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
ELEMENTS FLETCHER
TEMPORARIES
R N
R D
R FV
R DX
R DY
R DV
R DW
INDIVIDUALS
T 2PR
F XX * YY
G XX YY
G YY XX
H XX YY 1.0
T SQ
F XX * XX
G XX XX + XX
H XX XX 2.0
T SPEC
A N XX * VV + YY * WW
A D XX * XX + YY * YY
A FV N * N / D
A DX 2.0 * ( N * VV - FV * XX ) / D
A DY 2.0 * ( N * WW - FV * YY ) / D
A DV 2.0 * N * XX / D
A DW 2.0 * N * YY / D
F FV
G XX DX
G YY DY
G VV DV
G WW DW
H XX XX 2.0 * ( VV * VV - DX * XX - FV ) / D
H+ - 2.0 * XX * DX / D
H XX YY 2.0 * ( WW * VV - DY * XX ) / D
H+ - 2.0 * YY * DX / D
H XX VV 2.0 * ( XX * VV + N - DV * XX ) / D
H XX WW 2.0 * ( YY * VV - DW * XX ) / D
H YY YY 2.0 * ( WW * WW - DY * YY - FV ) / D
H+ - 2.0 * YY * DY / D
H YY VV 2.0 * ( XX * WW - DV * YY ) / D
H YY WW 2.0 * ( YY * WW + N - DW * YY ) / D
H VV VV 2.0 * XX * XX / D
H VV WW 2.0 * YY * XX / D
H WW WW 2.0 * YY * YY / D
ENDATA