POLAK4.SIF

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* SET UP THE INITIAL DATA *
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NAME          POLAK4

*   Problem :
*   *********

*   A nonlinear minmax problem in two 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  LQR2-AN-3-3

VARIABLES

    X1
    X2
    U

GROUPS

 XN OBJ       U         1.0

 XL F1        U         -1.0           X1        -1.0
 XL F2        U         -1.0 
 XL F3        U         -1.0 

CONSTANTS

    POLAK4    F1        1.0
    POLAK4    F2        0.01
    POLAK4    F3        100000.0

BOUNDS

*   All variables are free

 FR POLAK4    'DEFAULT'

START POINT

    POLAK4    X1        0.9
    POLAK4    X2        0.1

ELEMENT TYPE

 EV SSQ       XX
 EP SSQ       S

ELEMENT USES

 T  X1SQ      SSQ
 V  X1SQ      XX                       X1
 P  X1SQ      S         0.0

 T  X2SQ      SSQ
 V  X2SQ      XX                       X2
 P  X2SQ      S         0.0

 T  X1M2SQ    SSQ
 V  X1M2SQ    XX                       X1
 P  X1M2SQ    S         2.0

GROUP USES

 XE F1        X1SQ      2.0            X2SQ      2.0
 XE F2        X1SQ      0.01           X2SQ      0.01
 XE F3        X1M2SQ    100000.0       X2SQ      1.0

OBJECT BOUND

*   Solution

*LO SOLTN               0.0

ENDATA

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* SET UP THE FUNCTION *
* AND RANGE ROUTINES  *
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ELEMENTS      POLAK4

INDIVIDUALS

 T  SSQ
 F                      ( XX - S ) ** 2
 G  XX                  2.0 * ( XX - S )
 H  XX        XX        2.0

ENDATA