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PROBPENL.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME PROBPENL
* Problem :
* *********
* The Probabilistic Penalty problem.
* This problem has N-1 trivial groups and 1 weighted least square group.
* Each of the first N-1 has 1 nonlinear element. The last one is
* linear.
* Source: problem 46 in
* Ph.L. Toint,
* "Test problems for partially separable optimization and results
* for the routine PSPMIN",
* Report 83/4, Department of Mathematics, FUNDP (Namur, B), 1983.
* SIF input: Ph. Toint, Dec 1989.
* classification OBR2-AN-V-0
* Number of variables
*IE N 10 $-PARAMETER
*IE N 50 $-PARAMETER
*IE N 100 $-PARAMETER
IE N 500 $-PARAMETER
* Other parameters
IE 1 1
IA N-1 N -1
RI RN-1 N-1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 N-1
XN G(I)
ND
DO I 1 N
XN G(N) X(I) 1.0
XN G(N) 'SCALE' 0.01
ND
CONSTANTS
X PROBPENL G(N) 1.0
BOUNDS
XL PROBPENL 'DEFAULT' -5.0
XU PROBPENL 'DEFAULT' 5.0
START POINT
XV PROBPENL 'DEFAULT' 0.5
ELEMENT TYPE
EV EXP2 V1 V2
EP EXP2 NG
ELEMENT USES
DO I 1 N-1
IA I+1 I 1
XT E(I) EXP2
ZV E(I) V1 X(I)
ZV E(I) V2 X(I+1)
ZP E(I) NG RN-1
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
DO I 1 N-1
XE G(I) E(I)
ND
XT G(N) L2
OBJECT BOUND
* Least square problems are bounded below by zero
LO PROBPENL 0.0
* Solution
*LO SOLTN(10) 1.7820896D-05
*LO SOLTN(50) 3.9184323D-06
*LO SOLTN(100) 1.9798020D-06
*LO SOLTN(500) ???
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS PROBPENL
TEMPORARIES
R FACT
R V1PV2
R EXPA
R OMX
R OMY
M EXP
INDIVIDUALS
T EXP2
A FACT 0.0001 / ( NG + 1.0 )
A V1PV2 V1 + V2
A EXPA FACT * EXP( - V1 * V2 )
A OMX 1.0 - V1 * V1PV2
A OMY 1.0 - V2 * V1PV2
F V1PV2 * EXPA
G V1 EXPA * OMY
G V2 EXPA * OMX
H V1 V1 - V2 * EXPA * ( OMY + 1.0 )
H V1 V2 EXPA * ( V2 * V1 * V1 + V2 * V2 * V1
H+ - V1 - V1 - V2 - V2 )
H V2 V2 - V1 * EXPA * ( OMX + 1.0 )
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS PROBPENL
INDIVIDUALS
* Least squares
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA