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POLAK6.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME POLAK6
* Problem :
* *********
* A nonlinear minmax problem in four variables. This is a variation
* on problem ROSENMMX.
* Source:
* E. Polak, D.H. Mayne and J.E. Higgins,
* "Superlinearly convergent algorithm for min-max problems"
* JOTA 69, pp. 407-439, 1991.
* SIF input: Ph. Toint, Nov 1993.
* classification LOR2-AN-5-4
VARIABLES
X1
X2
X3
X4
U
GROUPS
XN OBJ U 1.0
XL F1 U -1.0
XL F1 X1 -5.0 X2 -5.0
XL F1 X3 -21.0 X4 7.0
XL F2 U -1.0
XL F2 X1 5.0 X2 -15.0
XL F2 X3 -11.0 X4 -3.0
XL F3 U -1.0
XL F3 X1 -15.0 X2 -5.0
XL F3 X3 -21.0 X4 -3.0
XL F4 U -1.0
XL F4 X1 15.0 X2 -15.0
XL F4 X3 -21.0 X4 -3.0
CONSTANTS
POLAK6 F2 80.0
POLAK6 F3 100.0
POLAK6 F4 50.0
BOUNDS
* All variables are free
FR POLAK6 'DEFAULT'
ELEMENT TYPE
EV SQ XX
EV EL42 XX YY
EV EL442 XX YY
EV EL442 ZZ
EV EL4 XX
EV EL44 XX YY
ELEMENT USES
T E1 EL42
V E1 XX X1
V E1 YY X4
T E2 EL442
V E2 XX X2
V E2 YY X1
V E2 ZZ X4
T E3 EL4
V E3 XX X4
T E4 EL44
V E4 XX X1
V E4 YY X4
T X3SQ SQ
V X3SQ XX X3
T X4SQ SQ
V X4SQ XX X4
GROUP USES
E F1 E1 E2
E F1 X3SQ 2.0 X4SQ
E F1 E3 5.0 E4 5.0
E F2 E1 11.0 E2 11.0
E F2 X3SQ 12.0 X4SQ 11.0
E F2 E3 -5.0 E4 15.0
E F3 E1 11.0 E2 21.0
E F3 X3SQ 12.0 X4SQ 21.0
E F3 E3 15.0 E4 5.0
E F4 E1 11.0 E2 11.0
E F4 X3SQ 12.0 X4SQ
E F4 E3 -15.0 E4 15.0
OBJECT BOUND
* Solution at ( 0, 1, 2, -1 )
*LO SOLTN -44.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS POLAK6
TEMPORARIES
R A
R B
R C
R DCDY
R DADY
R DADZ
R DCDZ
R D2CDZZ
R D2ADYY
R D2ADYZ
R D2ADZZ
INDIVIDUALS
T EL42
A B YY + 1.0
A A XX - B ** 4
F A * A
G XX 2.0 * A
G YY - 8.0 * A * B ** 3
H XX XX 2.0
H XX YY - 8.0 * B ** 3
H YY YY 32.0 * B ** 6 - 24.0 * A * B ** 2
T EL442
A B ZZ + 1.0
A C YY - B ** 4
A DCDZ - 4.0 * B ** 3
A D2CDZZ - 12.0 * B ** 2
A A XX - C ** 4
A DADY - 4.0 * C ** 3
A DADZ DADY * DCDZ
A D2ADYY - 12.0 * C ** 2
A D2ADYZ D2ADYY * DCDZ
A D2ADZZ D2ADYZ * DCDZ + DADY * D2CDZZ
F A * A
G XX 2.0 * A
G YY 2.0 * A * DADY
G ZZ 2.0 * A * DADZ
H XX XX 2.0
H XX YY 2.0 * DADY
H XX ZZ 2.0 * DADZ
H YY YY 2.0 * ( DADY * DADY + A * D2ADYY )
H YY ZZ 2.0 * ( DADZ * DADY + A * D2ADYZ )
H ZZ ZZ 2.0 * ( DADZ * DADZ + A * D2ADZZ )
T EL4
A B XX + 1.0
F B ** 4
G XX 4.0 * B ** 3
H XX XX 12.0 * B ** 2
T EL44
A B YY + 1.0
A A XX - B ** 4
F A ** 4
G XX 4.0 * A ** 3
G YY - 16.0 * ( A * B ) ** 3
H XX XX 12.0 * A ** 2
H XX YY - 48.0 * A ** 2 * B ** 3
H YY YY - 48.0 * ( A * B ) ** 2 *
H+ ( A - 4.0 * B ** 4 )
T SQ
F XX * XX
G XX XX + XX
H XX XX 2.0
ENDATA