MAXLIKA.SIF

***************************
* SET UP THE INITIAL DATA *
***************************

NAME          MAXLIKA

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

*   A variant of Hock and Schittkowski problem 105, where the
*   (inactive) inequality constraint is dropped.

*   Source:
*   Ph. Toint and A. Griewank.

*   SIF input: Ph. Toint, June 1990.

*   classification OBR2-AY-8-0

*   Constants

 IE 1                   1
 IE 235                 235

*   Problem dependent data

 RE Y1                  95.0
 RE Y2                  105.0
 RE Y3                  110.0
 RE Y4                  110.0
 RE Y5                  110.0
 RE Y6                  110.0
 RE Y7                  115.0
 RE Y8                  115.0
 RE Y9                  115.0
 RE Y10                 115.0
 RE Y11                 120.0
 RE Y12                 120.0
 RE Y13                 120.0
 RE Y14                 120.0
 RE Y15                 120.0
 RE Y16                 120.0
 RE Y17                 120.0
 RE Y18                 120.0
 RE Y19                 120.0
 RE Y20                 120.0
 RE Y21                 120.0
 RE Y22                 120.0
 RE Y23                 120.0
 RE Y24                 120.0
 RE Y25                 120.0
 RE Y26                 125.0
 RE Y27                 125.0
 RE Y28                 125.0
 RE Y29                 125.0
 RE Y30                 125.0
 RE Y31                 125.0
 RE Y32                 125.0
 RE Y33                 125.0
 RE Y34                 125.0
 RE Y35                 125.0
 RE Y36                 125.0
 RE Y37                 125.0
 RE Y38                 125.0
 RE Y39                 125.0
 RE Y40                 125.0
 RE Y41                 130.0
 RE Y42                 130.0
 RE Y43                 130.0
 RE Y44                 130.0
 RE Y45                 130.0
 RE Y46                 130.0
 RE Y47                 130.0
 RE Y48                 130.0
 RE Y49                 130.0
 RE Y50                 130.0
 RE Y51                 130.0
 RE Y52                 130.0
 RE Y53                 130.0
 RE Y54                 130.0
 RE Y55                 130.0
 RE Y56                 135.0
 RE Y57                 135.0
 RE Y58                 135.0
 RE Y59                 135.0
 RE Y60                 135.0
 RE Y61                 135.0
 RE Y62                 135.0
 RE Y63                 135.0
 RE Y64                 135.0
 RE Y65                 135.0
 RE Y66                 135.0
 RE Y67                 135.0
 RE Y68                 135.0
 RE Y69                 140.0
 RE Y70                 140.0
 RE Y71                 140.0
 RE Y72                 140.0
 RE Y73                 140.0
 RE Y74                 140.0
 RE Y75                 140.0
 RE Y76                 140.0
 RE Y77                 140.0
 RE Y78                 140.0
 RE Y79                 140.0
 RE Y80                 140.0
 RE Y81                 140.0
 RE Y82                 140.0
 RE Y83                 140.0
 RE Y84                 140.0
 RE Y85                 140.0
 RE Y86                 140.0
 RE Y87                 140.0
 RE Y88                 140.0
 RE Y89                 140.0
 RE Y90                 145.0
 RE Y91                 145.0
 RE Y92                 145.0
 RE Y93                 145.0
 RE Y94                 145.0
 RE Y95                 145.0
 RE Y96                 145.0
 RE Y97                 145.0
 RE Y98                 145.0
 RE Y99                 145.0
 RE Y100                145.0
 RE Y101                145.0
 RE Y102                150.0
 RE Y103                150.0
 RE Y104                150.0
 RE Y105                150.0
 RE Y106                150.0
 RE Y107                150.0
 RE Y108                150.0
 RE Y109                150.0
 RE Y110                150.0
 RE Y111                150.0
 RE Y112                150.0
 RE Y113                150.0
 RE Y114                150.0
 RE Y115                150.0
 RE Y116                150.0
 RE Y117                150.0
 RE Y118                150.0
 RE Y119                155.0
 RE Y120                155.0
 RE Y121                155.0
 RE Y122                155.0
 RE Y123                160.0
 RE Y124                160.0
 RE Y125                160.0
 RE Y126                160.0
 RE Y127                160.0
 RE Y128                160.0
 RE Y129                160.0
 RE Y130                160.0
 RE Y131                160.0
 RE Y132                160.0
 RE Y133                160.0
 RE Y134                160.0
 RE Y135                160.0
 RE Y136                160.0
 RE Y137                160.0
 RE Y138                160.0
 RE Y139                160.0
 RE Y140                160.0
 RE Y141                160.0
 RE Y142                160.0
 RE Y143                165.0
 RE Y144                165.0
 RE Y145                165.0
 RE Y146                165.0
 RE Y147                165.0
 RE Y148                165.0
 RE Y149                165.0
 RE Y150                165.0
 RE Y151                170.0
 RE Y152                170.0
 RE Y153                170.0
 RE Y154                170.0
 RE Y155                170.0
 RE Y156                170.0
 RE Y157                170.0
 RE Y158                170.0
 RE Y159                170.0
 RE Y160                170.0
 RE Y161                170.0
 RE Y162                170.0
 RE Y163                170.0
 RE Y164                170.0
 RE Y165                170.0
 RE Y166                170.0
 RE Y167                170.0
 RE Y168                175.0
 RE Y169                175.0
 RE Y170                175.0
 RE Y171                175.0
 RE Y172                175.0
 RE Y173                175.0
 RE Y174                175.0
 RE Y175                175.0
 RE Y176                180.0
 RE Y177                180.0
 RE Y178                180.0
 RE Y179                180.0
 RE Y180                180.0
 RE Y181                180.0
 RE Y182                185.0
 RE Y183                185.0
 RE Y184                185.0
 RE Y185                185.0
 RE Y186                185.0
 RE Y187                185.0
 RE Y188                190.0
 RE Y189                190.0
 RE Y190                190.0
 RE Y191                190.0
 RE Y192                190.0
 RE Y193                190.0
 RE Y194                190.0
 RE Y195                195.0
 RE Y196                195.0
 RE Y197                195.0
 RE Y198                195.0
 RE Y199                200.0
 RE Y200                200.0
 RE Y201                200.0
 RE Y202                205.0
 RE Y203                205.0
 RE Y204                205.0
 RE Y205                210.0
 RE Y206                210.0
 RE Y207                210.0
 RE Y208                210.0
 RE Y209                210.0
 RE Y210                210.0
 RE Y211                210.0
 RE Y212                210.0
 RE Y213                215.0
 RE Y214                220.0
 RE Y215                220.0
 RE Y216                220.0
 RE Y217                220.0
 RE Y218                220.0
 RE Y219                220.0
 RE Y220                230.0
 RE Y221                230.0
 RE Y222                230.0
 RE Y223                230.0
 RE Y224                230.0
 RE Y225                235.0
 RE Y226                240.0
 RE Y227                240.0
 RE Y228                240.0
 RE Y229                240.0
 RE Y230                240.0
 RE Y231                240.0
 RE Y232                240.0
 RE Y233                245.0
 RE Y234                250.0
 RE Y235                250.0

VARIABLES

    X1
    X2
    X3
    X4
    X5
    X6
    X7
    X8

GROUPS

 DO I         1                        235
 XN L(I)      'SCALE'   -1.0
 ND

BOUNDS

 LO MAXLIKA   X1        0.001
 UP MAXLIKA   X1        0.499

 LO MAXLIKA   X2        0.001
 UP MAXLIKA   X2        0.499

 LO MAXLIKA   X3        100.0
 UP MAXLIKA   X3        180.0

 LO MAXLIKA   X4        130.0
 UP MAXLIKA   X4        210.0

 LO MAXLIKA   X5        170.0
 UP MAXLIKA   X5        240.0

 LO MAXLIKA   X6        5.0
 UP MAXLIKA   X6        25.0

 LO MAXLIKA   X7        5.0
 UP MAXLIKA   X7        25.0

 LO MAXLIKA   X8        5.0
 UP MAXLIKA   X8        25.0


START POINT

    MAXLIKA   X1        0.1
    MAXLIKA   X2        0.2
    MAXLIKA   X3        100.0
    MAXLIKA   X4        125.0
    MAXLIKA   X5        175.0
    MAXLIKA   X6        11.2
    MAXLIKA   X7        13.2
    MAXLIKA   X8        15.8

ELEMENT TYPE

 EV AB        U                        V
 EV AB        W
 EP AB        Y

 EV C         U                        X
 EV C         S                        T
 IV C         Z                        V
 IV C         W
 EP C         Y

ELEMENT USES

 DO I         1                        235

 XT A(I)      AB
 ZV A(I)      U                        X1
 ZV A(I)      V                        X6
 ZV A(I)      W                        X3
 ZP A(I)      Y                        Y(I)

 XT B(I)      AB
 ZV B(I)      U                        X2
 ZV B(I)      V                        X7
 ZV B(I)      W                        X4
 ZP B(I)      Y                        Y(I)

 XT C(I)      C
 ZV C(I)      U                        X2
 ZV C(I)      X                        X1
 ZV C(I)      S                        X8
 ZV C(I)      T                        X5
 ZP C(I)      Y                        Y(I)

 ND

GROUP TYPE

 GV LN        GVAR

GROUP USES

 DO I         1                        235
 XT L(I)      LN
 XE L(I)      A(I)                     B(I)
 XE L(I)      C(I)
 ND

ENDATA

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

ELEMENTS      MAXLIKA

TEMPORARIES

 R  YMW
 R  YMWSQ
 R  VSQ
 R  VCB
 R  A
 R  DADV
 R  DADW
 R  D2ADV2
 R  D2ADVW
 R  D2ADW2
 R  E
 R  DEDV
 R  DEDW
 R  B
 R  DBDV
 R  DBDW
 R  DBDZ
 R  D2BDVZ
 R  D2BDWZ
 R  D2BDV2
 R  D2BDVW
 R  D2BDW2

 M  EXP

INDIVIDUALS

*   First element type

 T  AB

 A  YMW                 Y - W
 A  YMWSQ               YMW * YMW
 A  VSQ                 V * V
 A  VCB                 VSQ * V

 A  A                   - YMWSQ / ( 2.0 * VSQ )
 A  DADV                YMWSQ / VCB
 A  DADW                YMW / VSQ
 A  D2ADV2              -3.0 * YMWSQ / ( VSQ * VSQ )
 A  D2ADVW              -2.0 * YMW / VCB
 A  D2ADW2              - 1.0 / VSQ

 A  E                   EXP( A )
 A  DEDV                E * DADV
 A  DEDW                E * DADW

 A  B                   U * E
 A  DBDV                B * DADV
 A  DBDW                B * DADW
 A  D2BDV2              DBDV * DADV + B * D2ADV2
 A  D2BDVW              DBDW * DADV + B * D2ADVW
 A  D2BDW2              DBDW * DADW + B * D2ADW2

 F                      B / V
 G  U                   E / V
 G  V                   ( DBDV - B / V ) / V
 G  W                   DBDW / V
 H  U         V         ( DEDV - E / V ) / V
 H  U         W         DEDW / V
 H  V         V         ( D2BDV2 -  DBDV / V + B / VSQ ) / V
 H+                     - ( DBDV - B / V ) / VSQ
 H  V         W         ( D2BDVW - DBDW / V ) / V
 H  W         W         D2BDW2 / V

*   Second element type

 T  C

 R  Z         U         1.0            X         1.0
 R  V         S         1.0
 R  W         T         1.0

 A  YMW                 Y - W
 A  YMWSQ               YMW * YMW
 A  VSQ                 V * V
 A  VCB                 VSQ * V

 A  A                   - YMWSQ / ( 2.0 * VSQ )
 A  DADV                YMWSQ / VCB
 A  DADW                YMW / VSQ
 A  D2ADV2              -3.0 * YMWSQ / ( VSQ * VSQ )
 A  D2ADVW              -2.0 * YMW / VCB
 A  D2ADW2              - 1.0 / VSQ

 A  E                   EXP( A )
 A  DEDV                E * DADV
 A  DEDW                E * DADW

 A  B                   (1.0 - Z) * E
 A  DBDZ                - E
 A  DBDV                B * DADV
 A  DBDW                B * DADW
 A  D2BDVZ              - DEDV
 A  D2BDWZ              - DEDW
 A  D2BDV2              DBDV * DADV + B * D2ADV2
 A  D2BDVW              DBDW * DADV + B * D2ADVW
 A  D2BDW2              DBDW * DADW + B * D2ADW2

 F                      B / V
 G  Z                   DBDZ / V
 G  V                   ( DBDV - B / V ) / V
 G  W                   DBDW / V
 H  Z         V         ( DEDV - E / V ) / V
 H  Z         W         D2BDWZ / V
 H  V         V         ( D2BDV2 -  DBDV / V + B / VSQ ) / V
 H+                     - ( DBDV - B / V ) / VSQ
 H  V         W         ( D2BDVW - DBDW / V ) / V
 H  W         W         D2BDW2 / V

ENDATA

*********************
* SET UP THE GROUPS *
* ROUTINE           *
*********************

GROUPS        MAXLIKA

TEMPORARIES

 M  LOG

INDIVIDUALS

 T  LN
 F                      LOG ( GVAR * 0.39894228 )
 G                      1.0 / GVAR
 H                      - 1.0 / GVAR**2

ENDATA