POLAK1.SIF

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* SET UP THE INITIAL DATA *
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NAME          POLAK1

*   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  LOR2-AN-3-2

VARIABLES

    X1
    X2
    U

GROUPS

 XN OBJ       U         1.0

 XL F1        U         -1.0 
 XL F2        U         -1.0 

BOUNDS

*   All variables are free

 FR POLAK1    'DEFAULT'

START POINT

    POLAK1    X1        50.0
    POLAK1    X2        0.05

ELEMENT TYPE

 EV EL        XX1                      XX2
 EP EL        S

ELEMENT USES

 T  E1        EL
 V  E1        XX1                      X1
 V  E1        XX2                      X2
 P  E1        S         -1.0

 T  E2        EL
 V  E2        XX1                      X1
 V  E2        XX2                      X2
 P  E2        S         1.0

GROUP USES

 E  F1        E1
 E  F2        E2


OBJECT BOUND

*   Solution

*LO SOLTN               2.7182818

ENDATA

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* SET UP THE FUNCTION *
* AND RANGE ROUTINES  *
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ELEMENTS      POLAK1

TEMPORARIES

 R  TX1
 R  DTX1
 R  TX2
 R  DTX2
 R  EARG

 M  EXP

INDIVIDUALS

 T  EL
 A  TX1                 0.001 * XX1 * XX1
 A  DTX1                0.002 * XX1
 A  TX2                 ( XX2 + S ) ** 2
 A  DTX2                2.0 * ( XX2 + S )
 A  EARG                EXP( TX1 + TX2 )
 F                      EARG
 G  XX1                 DTX1 * EARG
 G  XX2                 DTX2 * EARG
 H  XX1       XX1       ( 0.002 + DTX1 * DTX1 ) * EARG
 H  XX1       XX2       DTX1 * DTX2 * EARG
 H  XX2       XX2       ( 2.0 + DTX2 * DTX2 ) * EARG

ENDATA