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BT4.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME BT4
* Problem :
* *********
* Source: a variant of problem 4 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 original problem seems to be unbounded. The contribution of
* x3 in the first constraint has been squared instead of cubed.
* The problem is not convex.
* SIF input: Ph. Toint, June 1993.
* classification QQR2-AN-3-2
VARIABLES
X1
X2
X3
GROUPS
N OBJ X1 1.0 X2 -1.0
E CON1
E CON2 X1 1.0 X2 1.0
E CON2 X3 1.0
CONSTANTS
BT4 CON1 25.0
BT4 CON2 1.0
BOUNDS
FR BT4 'DEFAULT'
START POINT
* Start 1
*XV BT4 X1 3.1494
*XV BT4 X2 1.4523
*XV BT4 X3 -3.6017
* Start 2
*XV BT4 X1 3.122
*XV BT4 X2 1.489
*XV BT4 X3 -3.611
* Start 3
*XV BT4 X1 -0.94562
*XV BT4 X2 -2.35984
*XV BT4 X3 4.30546
* Solution proposed in the paper for the original problem
XV BT4 X1 4.0382
XV BT4 X2 -2.9470
XV BT4 X3 -0.09115
ELEMENT TYPE
EV SQ X
EV CB X
ELEMENT USES
T X1SQ SQ
V X1SQ X X1
T X2SQ SQ
V X2SQ X X2
T X2CB CB
V X2CB X X2
T X3SQ SQ
V X3SQ X X3
GROUP USES
E OBJ X2CB
E CON1 X1SQ X2SQ
E CON1 X3SQ
OBJECT BOUND
* Solution
*LO SOLTN 3.28903771
*LO SOLTN -45.510551
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS BT4
INDIVIDUALS
T SQ
F X * X
G X 2.0 * X
H X X 2.0
T CB
F X**3
G X 3.0 * X**2
H X X 6.0 * X
ENDATA