POLAK3.SIF

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* SET UP THE INITIAL DATA *
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NAME          POLAK3

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

*   A nonlinear minmax problem in eleven variables.

*   Note: the original statement of the problem contains an inconsistant
*         index i.  This has been replaced by 1, assuming a very common typo.
*         But the optimal solution of the resulting problem differs from that
*         quoted in the source. 

*   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-12-10

 IE 1                   1
 IE 10                  10
 IE 11                  11

VARIABLES

 DO I         1                        11
 X  X(I)
 OD I

    U

GROUPS

 XN OBJ       U         1.0

 DO I         1                        10
 XL F(I)      U         -1.0 
 OD I

BOUNDS

*   All variables are free

 FR POLAK3    'DEFAULT'

START POINT

 V  POLAK3    'DEFAULT' 1.0

ELEMENT TYPE

 EV EL        XX
 EP EL        A                        B

ELEMENT USES

 DO I         1                        10
 IA I-1       I         -1
 RI RI-1      I-1
 DO J         1                        11
 IA J-1       J         -1
 RI RJ-1      J
 XT E(I,J)    EL
 ZV E(I,J)    XX                       X(J)
 ZP E(I,J)    A                        RI-1
 ZP E(I,J)    B                        RJ-1
 OD J
 OD I

GROUP USES

 DO I         1                        10
 DO J         1                        11
 RI RJ        J
 RD 1/J       RJ        1.0
 ZE F(I)      E(I,J)                   1/J
 OD J
 OD I

OBJECT BOUND

*   Solution

*LO SOLTN                5.93300252

ENDATA

***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES  *
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ELEMENTS      POLAK3

TEMPORARIES

 R  V
 R  EV

 M  EXP

INDIVIDUALS

 T  EL
 A  V                   XX - SIN( A + B + B )
 A  EV                  EXP( V * V )
 F                      EV
 G  XX                  2.0 * V * EV
 H  XX        XX        ( 4.0 * V * V  + 2.0 ) * EV

ENDATA