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POLAK2.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME POLAK2
* Problem :
* *********
* A nonlinear minmax problem in ten variables.
* 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-11-2
IE 1 1
IE 10 10
VARIABLES
DO I 1 10
X X(I)
OD I
U
GROUPS
XN OBJ U 1.0
XL F1 U -1.0
XL F2 U -1.0
BOUNDS
* All variables are free
FR POLAK2 'DEFAULT'
START POINT
V POLAK2 'DEFAULT' 0.1
POLAK2 X1 100.0
ELEMENT TYPE
EV EL XX1 XX2
EV EL XX3 XX4
EV EL XX5 XX6
EV EL XX7 XX8
EV EL XX9 XX10
EP EL P
ELEMENT USES
T E1 EL
V E1 XX1 X1
V E1 XX2 X2
V E1 XX3 X3
V E1 XX4 X4
V E1 XX5 X5
V E1 XX6 X6
V E1 XX7 X7
V E1 XX8 X8
V E1 XX9 X9
V E1 XX10 X10
P E1 P 2.0
T E2 EL
V E2 XX1 X1
V E2 XX2 X2
V E2 XX3 X3
V E2 XX4 X4
V E2 XX5 X5
V E2 XX6 X6
V E2 XX7 X7
V E2 XX8 X8
V E2 XX9 X9
V E2 XX10 X10
P E2 P -2.0
GROUP USES
E F1 E1
E F2 E2
OBJECT BOUND
* Solution
*LO SOLTN 54.598146
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS POLAK2
TEMPORARIES
R A
R EA
M EXP
INDIVIDUALS
T EL
A A 1.0D-8 * XX1 * XX1 + ( XX2 + P ) **2
A A A + XX3 * XX3 + 4.0 * XX4 * XX4
A A A + XX5 * XX5 + XX6 * XX6 + XX7 * XX7
A A A + XX8 * XX8 + XX9 * XX9 + XX10 * XX10
A EA EXP( A )
F EA
G XX1 2.0D-8 * XX1 * EA
G XX2 2.0 * ( XX2 + P ) * EA
G XX3 2.0 * XX3 * EA
G XX4 8.0 * XX4 * EA
G XX5 2.0 * XX5 * EA
G XX6 2.0 * XX6 * EA
G XX7 2.0 * XX7 * EA
G XX8 2.0 * XX8 * EA
G XX9 2.0 * XX9 * EA
G XX10 2.0 * XX10 * EA
H XX1 XX1 2.0D-8 * EA * ( 1.0 + 2.0D-8 * XX1 ** 2 )
H XX1 XX2 4.0D-8 * XX1 * ( XX2 + P ) * EA
H XX1 XX3 4.0D-8 * XX1 * XX3 * EA
H XX1 XX4 1.6D-7 * XX1 * XX4 * EA
H XX1 XX5 4.0D-8 * XX1 * XX5 * EA
H XX1 XX6 4.0D-8 * XX1 * XX6 * EA
H XX1 XX7 4.0D-8 * XX1 * XX7 * EA
H XX1 XX8 4.0D-8 * XX1 * XX8 * EA
H XX1 XX9 4.0D-8 * XX1 * XX9 * EA
H XX1 XX10 4.0D-8 * XX1 * XX10 * EA
H XX2 XX2 2.0 * EA * ( 1.0 + 2.0 * ( XX2 + P)**2 )
H XX2 XX3 4.0 * ( XX2 + P ) * XX3 * EA
H XX2 XX4 16.0 * ( XX2 + P ) * XX4 * EA
H XX2 XX5 4.0 * ( XX2 + P ) * XX5 * EA
H XX2 XX6 4.0 * ( XX2 + P ) * XX6 * EA
H XX2 XX7 4.0 * ( XX2 + P ) * XX7 * EA
H XX2 XX8 4.0 * ( XX2 + P ) * XX8 * EA
H XX2 XX9 4.0 * ( XX2 + P ) * XX9 * EA
H XX2 XX10 4.0 * ( XX2 + P ) * XX10 * EA
H XX3 XX3 2.0 * EA * ( 1.0 + 2.0 * XX3 * XX3 )
H XX3 XX4 16.0 * XX3 * XX4 * EA
H XX3 XX5 4.0 * XX3 * XX5 * EA
H XX3 XX6 4.0 * XX3 * XX6 * EA
H XX3 XX7 4.0 * XX3 * XX7 * EA
H XX3 XX8 4.0 * XX3 * XX8 * EA
H XX3 XX9 4.0 * XX3 * XX9 * EA
H XX3 XX10 4.0 * XX3 * XX10 * EA
H XX4 XX4 8.0 * EA * ( 1.0 + 8.0 * XX4 * XX4 )
H XX4 XX5 16.0 * XX4 * XX5 * EA
H XX4 XX6 16.0 * XX4 * XX6 * EA
H XX4 XX7 16.0 * XX4 * XX7 * EA
H XX4 XX8 16.0 * XX4 * XX8 * EA
H XX4 XX9 16.0 * XX4 * XX9 * EA
H XX4 XX10 16.0 * XX4 * XX10 * EA
H XX5 XX5 2.0 * EA * ( 1.0 + 2.0 * XX5 * XX5 )
H XX5 XX6 4.0 * XX5 * XX6 * EA
H XX5 XX7 4.0 * XX5 * XX7 * EA
H XX5 XX8 4.0 * XX5 * XX8 * EA
H XX5 XX9 4.0 * XX5 * XX9 * EA
H XX5 XX10 4.0 * XX5 * XX10 * EA
H XX6 XX6 2.0 * EA * ( 1.0 + 2.0 * XX6 * XX6 )
H XX6 XX7 4.0 * XX6 * XX7 * EA
H XX6 XX8 4.0 * XX6 * XX8 * EA
H XX6 XX9 4.0 * XX6 * XX9 * EA
H XX6 XX10 4.0 * XX6 * XX10 * EA
H XX7 XX7 2.0 * EA * ( 1.0 + 2.0 * XX7 * XX7 )
H XX7 XX8 4.0 * XX7 * XX8 * EA
H XX7 XX9 4.0 * XX7 * XX9 * EA
H XX7 XX10 4.0 * XX7 * XX10 * EA
H XX8 XX8 2.0 * EA * ( 1.0 + 2.0 * XX8 * XX8 )
H XX8 XX9 4.0 * XX8 * XX9 * EA
H XX8 XX10 4.0 * XX8 * XX10 * EA
H XX9 XX9 2.0 * EA * ( 1.0 + 2.0 * XX9 * XX9 )
H XX9 XX10 4.0 * XX9 * XX10 * EA
H XX10 XX10 2.0 * EA * ( 1.0 + 2.0 * XX10 * XX10 )
ENDATA