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KOWOSB.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME KOWOSB
* Problem :
* *********
* A problem arising in the analysis of kinetic data for an enzyme
* reaction, known under the name of Kowalik and Osborne problem
* in 4 variables.
* Source: Problem 15 in
* J.J. More', B.S. Garbow and K.E. Hillstrom,
* "Testing Unconstrained Optimization Software",
* ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.
* SIF input: Ph. Toint, Dec 1989.
* classification SUR2-MN-4-0
* This function is a nonlinear least squares with 11 groups. Each
* group has a linear and a nonlinear element.
* Number of groups
IE M 11
* Useful parameters
IE 1 1
VARIABLES
X1
X2
X3
X4
GROUPS
DO I 1 M
XN G(I)
ND
CONSTANTS
KOWOSB G1 0.1957
KOWOSB G2 0.1947
KOWOSB G3 0.1735
KOWOSB G4 0.1600
KOWOSB G5 0.0844
KOWOSB G6 0.0627
KOWOSB G7 0.0456
KOWOSB G8 0.0342
KOWOSB G9 0.0323
KOWOSB G10 0.0235
KOWOSB G11 0.0246
BOUNDS
* All variables are free
FR KOWOSB 'DEFAULT'
START POINT
* Starting for MGH#15 and Buckley#31
KOWOSB X1 0.25
KOWOSB X2 0.39
KOWOSB X3 0.415
KOWOSB X4 0.39
ELEMENT TYPE
EV KWO V1 V2
EV KWO V3 V4
EP KWO U
ELEMENT USES
DO I 1 M
XT E(I) KWO
ZV E(I) V1 X1
ZV E(I) V2 X2
ZV E(I) V3 X3
ZV E(I) V4 X4
ND
P E1 U 4.0
P E2 U 2.0
P E3 U 1.0
P E4 U 0.5
P E5 U 0.25
P E6 U 0.167
P E7 U 0.125
P E8 U 0.1
P E9 U 0.0833
P E10 U 0.0714
P E11 U 0.0624
GROUP TYPE
GV L2 GVAR
GROUP USES
DO I 1 M
XT G(I) L2
XE G(I) E(I)
ND
OBJECT BOUND
* Least square problems are bounded below by zero
LO KOWOSB 0.0
* Solution
*LO SOLTN 0.00102734
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS KOWOSB
TEMPORARIES
R USQ
R B1
R B2
R B2SQ
R B2CB
R UV1
R UB1
R T1
R T2
INDIVIDUALS
* Kowalik and Osborne function
T KWO
A USQ U * U
A B1 USQ + U * V2
A B2 USQ + U * V3 + V4
A B2SQ B2 * B2
A B2CB B2 * B2SQ
A UV1 U * V1
A UB1 U * B1
A T1 B1 / B2SQ
A T2 2.0 / B2CB
F V1 * B1 / B2
G V1 B1 / B2
G V2 UV1 / B2
G V3 - UV1 * T1
G V4 - V1 * T1
H V1 V2 U / B2
H V1 V3 - UB1 / B2SQ
H V1 V4 - T1
H V2 V3 - UV1 * U / B2SQ
H V2 V4 - UV1 / B2SQ
H V3 V3 T2 * UV1 * UB1
H V3 V4 T2 * UV1 * B1
H V4 V4 T2 * V1 * B1
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS KOWOSB
INDIVIDUALS
* Least-square groups
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA