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NONDIA.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME NONDIA
* Problem :
* --------
* The Shanno nondiagonal extension of Rosenbrock function.
* Source:
* D. Shanno,
* " On Variable Metric Methods for Sparse Hessians II: the New
* Method",
* MIS Tech report 27, University of Arizona (Tucson, UK), 1978.
* See also Buckley #37 (p. 76) and Toint #15.
* SIF input: Ph. Toint, Dec 1989.
* classification SUR2-AN-V-0
* Number of variables
*IE N 10 $-PARAMETER
*IE N 20 $-PARAMETER
*IE N 30 $-PARAMETER
*IE N 50 $-PARAMETER
*IE N 90 $-PARAMETER
*IE N 100 $-PARAMETER
*IE N 500 $-PARAMETER
*IE N 1000 $-PARAMETER original value
IE N 5000 $-PARAMETER
*IE N 10000 $-PARAMETER
* Other parameter definitions
IE 1 1
IE 2 2
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
XN SQ(1) X(1) 1.0
DO I 2 N
XN SQ(I) X(1) 1.0
XN SQ(I) 'SCALE' 0.01
ND
CONSTANTS
NONDIA SQ1 1.0
BOUNDS
* defaults = free variables
FR NONDIA 'DEFAULT'
START POINT
DO I 1 N
X NONDIA X(I) -1.0
ND
ELEMENT TYPE
EV ETYPE V1
EP ETYPE GAMMA
ELEMENT USES
DO I 2 N
* element type assignment
XT ELA(I) ETYPE
* problem to elemental variables assignment
IA J I -1
ZV ELA(I) V1 X(J)
* element parameter value
XP ELA(I) GAMMA 2.0
ND
GROUP TYPE
GV L2 GVAR
GROUP USES
XT SQ(1) L2
DO I 2 N
XT SQ(I) L2
XE SQ(I) ELA(I)
ND
OBJECT BOUND
* Least square problems are bounded below by zero
LO NONDIA 0.0
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS NONDIA
TEMPORARIES
I IGAMMA
INDIVIDUALS
T ETYPE
A IGAMMA GAMMA
F - V1 ** IGAMMA
G V1 - GAMMA * V1 ** ( IGAMMA - 1 )
H V1 V1 - GAMMA * ( GAMMA - 1.0 ) *
H+ V1 ** ( IGAMMA - 2 )
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS NONDIA
INDIVIDUALS
T L2
F GVAR * GVAR
G GVAR + GVAR
H 2.0
ENDATA