BT5.SIF

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* SET UP THE INITIAL DATA *
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NAME          BT5

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

*   Source: problem 5 in
*   P.T. Boggs and J.W. Tolle,
*   "A strategy for global convergence in a sequential 
*    quadratic programming algorithm",
*   SINUM 26(3), pp. 600-623, 1989.

*   The problem as stated in the paper seems to contain a typo.
*   The sign of the x3 squared term in the first constraint has been
*   set to + instead of - in order to ensdure that the problem is 
*   bounded below and the optimal point stated recovered.

*   The problem is not convex.

*   SIF input: Ph. Toint, June 1993.

*   classification QQR2-AN-3-2

VARIABLES

    X1
    X2
    X3

GROUPS

 N  OBJ

 E  CON1
 E  CON2      X1        8.0            X2        14.0
 E  CON2      X3        7.0

CONSTANTS

    BT5       OBJ       -1000.0
    BT5       CON1      25.0
    BT5       CON2      56.0

BOUNDS

 FR BT5       'DEFAULT'

START POINT

* Start 1

 XV BT5       'DEFAULT' 2.0

* Start 2

*XV BT5       'DEFAULT' 20.0

* Start 3

*XV BT5       'DEFAULT' 80.0

*XV BT5       X1        7.0
*XV BT5       X2        7.0
*XV BT5       X3        7.0
*XV BT5       X4        0.0
*XV BT5       X5        0.0

ELEMENT TYPE

 EV SQ        X
 EV 2PR       X                        Y

ELEMENT USES

 T  X1SQ      SQ
 V  X1SQ      X                        X1

 T  X2SQ      SQ
 V  X2SQ      X                        X2

 T  X3SQ      SQ
 V  X3SQ      X                        X3

 T  X1X2      2PR
 V  X1X2      X                        X1
 V  X1X2      Y                        X2

 T  X1X3      2PR
 V  X1X3      X                        X1
 V  X1X3      Y                        X3

GROUP USES

 E  OBJ       X1SQ      -1.0           X3SQ      -1.0
 E  OBJ       X2SQ      -2.0           X1X2      -1.0
 E  OBJ       X1X3      -1.0

 E  CON1      X1SQ                     X2SQ
 E  CON1      X3SQ

OBJECT BOUND

*   Solution            

*LO SOLTN               961.71517219

ENDATA

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* SET UP THE FUNCTION *
* AND RANGE ROUTINES  *
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ELEMENTS      BT5

INDIVIDUALS

 T  SQ
 F                      X * X
 G  X                   2.0 * X
 H  X         X         2.0

 T  2PR
 F                      X * Y
 G  X                   Y
 G  Y                   X
 H  X         Y         1.0

ENDATA