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LISWET8.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME LISWET8
* Problem :
* *********
* A k-convex approximation problem posed as a
* convex quadratic problem, with variable dimensions.
* Formulation:
* -----------
* n+k 2
* minimize 1/2 sum ( x - c )
* i=1 i i
* subject to
* k k-i
* sum ( k ) ( -1 ) x > 0
* i=0 ( i ) j+i =
* where c = g( t ) + small perturbation, t = (i-1)/(n+k-1)
* i i i
* Case 8: g(t) = sin(2 pi t)
* NB. Perturbations are not random as Li and Swetits's
* random number generator is undefined.
* Source:
* W. Li and J. Swetits,
* "A Newton method for convex regression, data smoothing and
* quadratic programming with bounded constraints",
* SIAM J. Optimization 3 (3) pp 466-488, 1993.
* SIF input: Nick Gould, August 1994.
* classification QLR2-AN-V-V
*IE N 100 $-PARAMETER 103 variables original value
*IE K 3 $-PARAMETER original value
*IE N 100 $-PARAMETER 104 variables
*IE K 4 $-PARAMETER
*IE N 100 $-PARAMETER 105 variables
*IE K 5 $-PARAMETER
*IE N 100 $-PARAMETER 106 variables
*IE K 6 $-PARAMETER
*IE N 400 $-PARAMETER 402 variables
*IE K 2 $-PARAMETER
*IE N 400 $-PARAMETER 403 variables
*IE K 3 $-PARAMETER
*IE N 2000 $-PARAMETER 2001 variables
*IE K 1 $-PARAMETER
IE N 2000 $-PARAMETER 2002 variables
IE K 2 $-PARAMETER
*IE N 10000 $-PARAMETER 10001 variables
*IE K 1 $-PARAMETER
*IE N 10000 $-PARAMETER 10002 variables
*IE K 2 $-PARAMETER
* Constants
IE 0 0
IE 1 1
RE ONE 1.0
RE HALF 0.5
* Set some useful parameters
I+ N+K N K
IA N+K-1 N+K -1
RI RN+K-1 N+K-1
RE CONST 0.0
* Binomial coefficients
A= B(0) ONE
DO I 1 K
IA I-1 I -1
RI RI I
A* B(I) B(I-1) RI
ND
* (-1)^K * Binomial coefficients
A= C(0) ONE
R= PLUSMINUS ONE
DO I 1 K
I- K-I K I
RM PLUSMINUS PLUSMINUS -1.0
A/ C(I) B(K) B(I)
A/ C(I) C(I) B(K-I)
A* C(I) C(I) PLUSMINUS
ND
VARIABLES
DO I 1 N+K
X X(I)
ND
GROUPS
* Objective linear coefficients
DO I 1 N+K
IA I-1 I -1
RI RI I
RI RI-1 I-1
R/ TI RI-1 RN+K-1
RF PI/4 ARCTAN 1.0
RM 2PI PI/4 8.0
R* 2PIT 2PI TI
R( GT SIN 2PIT
* Perturb by 0.1 * sin( i )
R( RANDOM SIN RI
RM RANDOM RANDOM 0.1
R+ CI GT RANDOM
RM -CI CI -1.0
R* -CI*CI -CI CI
R+ CONST CONST -CI*CI
ZN OBJ X(I) -CI
ND
* Divided difference constraints
DO J 1 N
I+ J+K J K
DO I 0 K
I- J+K-I J+K I
ZG CON(J) X(J+K-I) C(I)
OD I
OD J
CONSTANTS
R* CONST HALF CONST
Z LISWET8 OBJ CONST
BOUNDS
FR LISWET8 'DEFAULT'
ELEMENT TYPE
EV SQ X
ELEMENT USES
* The elements corresponding to the squre variables
DO I 1 N+K
XT XSQ(I) SQ
ZV XSQ(I) X X(I)
ND
GROUP USES
* The diagonal elements
DO I 1 N+K
XE OBJ XSQ(I)
OD I
OBJECT BOUND
* Solution
*LO SOLTN
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS LISWET8
INDIVIDUALS
T SQ
F 5.0D-1 * X * X
G X X
H X X 1.0D+0
ENDATA