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ELATTAR.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME ELATTAR
* Problem :
* *********
* A nonlinear minmax problem in six variables.
* The problem is nonconvex and has several local minima.
* Source:
* R.A. El-Attar, M. Vidyasagar and S.R.K. Dutta,
* "An algorithm for l_1-approximation",
* SINUM 16, pp.70-86, 1979.
* SIF input: Ph. Toint, Nov 1993.
* classification LOR2-AN-7-102
IE 1 1
IE 6 6
IE 51 51
RE T 0.0
DO I 1 51
* build the t_i
A= T(I) T
RA T T 0.1
* build the y_i
A( ETI EXP T(I)
AM Y(I) ETI 0.5
AM -2TI T(I) -2.0
R( E-2TI EXP -2TI
A- Y(I) Y(I) E-2TI
AM -3TI T(I) -3.0
R( E-3TI EXP -3TI
RM E-3TI/2 E-3TI 0.5
A+ Y(I) Y(I) E-3TI/2
RM -3TI/2 -3TI 0.5
R( E-3TI/2 EXP -3TI/2
AM 7TI T(I) 7.0
R( S7TI SIN 7TI
R* TT E-3TI/2 S7TI
RM TT TT 1.5
A+ Y(I) Y(I) TT
AM 5TI T(I) 5.0
RM -5TI/2 5TI -0.5
R( E-5TI/2 EXP -5TI/2
R( S5TI SIN 5TI
R* TT E-5TI/2 S5TI
A+ Y(I) Y(I) TT
OD I
VARIABLES
DO I 1 6
X X(I)
OD I
U
GROUPS
XN OBJ U 1.0
DO I 1 51
XL F(I) U -1.0
XL MF(I) U -1.0
OD I
CONSTANTS
DO I 1 51
Z ELATTAR F(I) Y(I)
AM -Y(I) Y(I) -1.0
Z ELATTAR MF(I) -Y(I)
OD I
BOUNDS
* All variables are free
FR ELATTAR 'DEFAULT'
START POINT
* The proposed starting point is (2,2,7,0,-2,1), but this one seems
* to be more interesting.
ELATTAR X1 -2.0
ELATTAR X2 -2.0
ELATTAR X3 7.0
ELATTAR X5 -2.0
ELATTAR X6 1.0
ELEMENT TYPE
EV ET1 V1 V2
EV ET1 V3 V4
EP ET1 T
EV ET2 V5 V6
EP ET2 T
ELEMENT USES
DO I 1 51
XT EL1(I) ET1
ZV EL1(I) V1 X1
ZV EL1(I) V2 X2
ZV EL1(I) V3 X3
ZV EL1(I) V4 X4
ZP EL1(I) T T(I)
XT EL2(I) ET2
ZV EL2(I) V5 X5
ZV EL2(I) V6 X6
ZP EL2(I) T T(I)
OD I
GROUP USES
DO I 1 51
XE F(I) EL1(I) 1.0 EL2(I) 1.0
XE MF(I) EL1(I) -1.0 EL2(I) -1.0
OD I
OBJECT BOUND
LO ELATTAR 0.0
* Solution
*LO SOLTN 0.1427066255
*LO SOLTN 74.206179244
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS ELATTAR
TEMPORARIES
R A
R B
R EA
R CB
R SB
R EACB
R EASB
R V1EACB
R V1EASB
M EXP
M SIN
M COS
INDIVIDUALS
T ET1
A A - V2 * T
A B V3 * T + V4
A EA EXP( A )
A CB COS( B )
A SB SIN( B )
A EACB EA * CB
A EASB EA * SB
A V1EACB V1 * EACB
A V1EASB V1 * EASB
F V1EACB
G V1 EACB
G V2 - T * V1EACB
G V3 - T * V1EASB
G V4 - V1EASB
H V1 V2 - T * EACB
H V1 V3 - T * EASB
H V1 V4 - EASB
H V2 V2 T * T * V1EACB
H V2 V3 T * T * V1EASB
H V2 V4 T * V1EASB
H V3 V3 - T * T * V1EACB
H V3 V4 - T * V1EACB
H V4 V4 - V1EACB
T ET2
A A - V6 * T
A EA EXP( A )
A B V5 * EA
F B
G V5 EA
G V6 - T * B
H V5 V6 - T * EA
H V6 V6 T * T * B
ENDATA