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LUKVLI6.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME LUKVLI6
* Problem :
* *********
* Source: Problem 5.6, Generalized Broyden banded function with
* exponential constraints, due to L. Luksan and J. Vlcek,
* "Sparse and partially separable test problems for
* unconstrained and equality constrained optimization",
* Technical Report 767, Inst. Computer Science, Academy of Sciences
* of the Czech Republic, 182 07 Prague, Czech Republic, 1999
* Equality constraints changed to inequalities
* SIF input: Nick Gould, April 2001
* classification OOR2-AY-V-V
* some useful parameters, including N, the number of variables.
*IE N 99 $-PARAMETER
*IE N 999 $-PARAMETER
IE N 9999 $-PARAMETER
*IE N 99999 $-PARAMETER
* other useful parameters
IE 0 0
IE 1 1
IE 2 2
IE 3 3
IE 4 4
IE 5 5
IE 6 6
I/ N/2 N 2
IA N+1 N 1
IA N-4 N -4
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
DO I 1 N
IA I+1 I 1
IA I-5 I -5
XN OBJ(I) X(I) 2.0
* Now for the fun part: Find MAX(1,I-5) and MIN(I+1,N)
I= A I-5
I= B 1
* this is how we find max(a,b) !!
* first add |a| + |b| to both
RI A A
R( ABSA ABS A
IR ABSA ABSA
RI B B
R( ABSB ABS B
IR ABSB ABSB
I+ ABSA+B ABSA ABSB
I+ A A ABSA+B
I+ B B ABSA+B
* only one of [a/b] and [b/a] is nonzero (unless a=b)
I/ A/B A B
I/ B/A B A
* form max(a,b) = (a.[a/b] + b.[b/a]) / ([a/b] + [b/a])
I+ SUM A/B B/A
I* A A A/B
I* B B B/A
I+ MAXA,B A B
I/ MAXA,B MAXA,B SUM
* subtract |a| + |b| to find the required minimum
I- MAXA,B MAXA,B ABSA+B
I= MAXI-5,1 MAXA,B
I= A I+1
I= B N
* this is how we find min(a,b) !!
* first set a <- - a and b <- - b
IM A A -1
IM B B -1
* now add |a| + |b| to both
RI A A
R( ABSA ABS A
IR ABSA ABSA
RI B B
R( ABSB ABS B
IR ABSB ABSB
I+ ABSA+B ABSA ABSB
I+ A A ABSA+B
I+ B B ABSA+B
* only one of [a/b] and [b/a] is nonzero (unless a=b)
I/ A/B A B
I/ B/A B A
* form max(a,b) = (a.[a/b] + b.[b/a]) / ([a/b] + [b/a])
I+ SUM A/B B/A
I* A A A/B
I* B B B/A
I+ MAXA,B A B
I/ MAXA,B MAXA,B SUM
* subtract |a| + |b| and negate to find the required minimum
I- MINA,B ABSA+B MAXA,B
I= MINI+1,N MINA,B
DO J MAXI-5,1 MINI+1,N
XN OBJ(I) X(J) 1.0
ND
DO K 1 N/2
IM 2K K 2
XG C(K) X(2K) 4.0
ND
CONSTANTS
DO I 1 N
X RHS OBJ(I) -1.0
ND
DO K 1 N/2
X RHS C(K) 3.0
ND
BOUNDS
FR BND 'DEFAULT'
START POINT
DO I 1 N
XV LUKVLI9 X(I) 3.0
ND
ELEMENT TYPE
EV SQR V
EV CUBE V
EV XEXP VM VP
EV XEXP V
IV XEXP U W
ELEMENT USES
DO I 1 N
XT S(I) SQR
ZV S(I) V X(I)
XT C(I) CUBE
ZV C(I) V X(I)
ND
DO K 1 N/2
IM 2K K 2
IA 2K-1 2K -1
IA 2K+1 2K 1
XT P(K) XEXP
ZV P(K) VM X(2K-1)
ZV P(K) V X(2K)
ZV P(K) VP X(2K+1)
ND
GROUP TYPE
GV L7/3 GVAR
GROUP USES
DO I 1 N
IA I+1 I 1
IA I-5 I -5
XT OBJ(I) L7/3
XE OBJ(I) C(I) 5.0
* Once again, find MAX(1,I-5) and MIN(I+1,N)
I= A I-5
I= B 1
* this is how we find max(a,b) !!
* first add |a| + |b| to both
RI A A
R( ABSA ABS A
IR ABSA ABSA
RI B B
R( ABSB ABS B
IR ABSB ABSB
I+ ABSA+B ABSA ABSB
I+ A A ABSA+B
I+ B B ABSA+B
* only one of [a/b] and [b/a] is nonzero (unless a=b)
I/ A/B A B
I/ B/A B A
* form max(a,b) = (a.[a/b] + b.[b/a]) / ([a/b] + [b/a])
I+ SUM A/B B/A
I* A A A/B
I* B B B/A
I+ MAXA,B A B
I/ MAXA,B MAXA,B SUM
* subtract |a| + |b| to find the required minimum
I- MAXA,B MAXA,B ABSA+B
I= MAXI-5,1 MAXA,B
I= A I+1
I= B N
* this is how we find min(a,b) !!
* first set a <- - a and b <- - b
IM A A -1
IM B B -1
* now add |a| + |b| to both
RI A A
R( ABSA ABS A
IR ABSA ABSA
RI B B
R( ABSB ABS B
IR ABSB ABSB
I+ ABSA+B ABSA ABSB
I+ A A ABSA+B
I+ B B ABSA+B
* only one of [a/b] and [b/a] is nonzero (unless a=b)
I/ A/B A B
I/ B/A B A
* form max(a,b) = (a.[a/b] + b.[b/a]) / ([a/b] + [b/a])
I+ SUM A/B B/A
I* A A A/B
I* B B B/A
I+ MAXA,B A B
I/ MAXA,B MAXA,B SUM
* subtract |a| + |b| and negate to find the required minimum
I- MINA,B ABSA+B MAXA,B
I= MINI+1,N MINA,B
DO J MAXI-5,1 MINI+1,N
XE OBJ(I) S(J) 1.0
ND
DO K 1 N/2
XE C(K) P(K) -1.0
ND
OBJECT BOUND
LO LUKVLI6 0.0
* Solution
*LO SOLTN 6.26382E+04
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS LUKVLI6
TEMPORARIES
R EXPW
R UEXPW
M EXP
INDIVIDUALS
T SQR
F V * V
G V 2.0 * V
H V V 2.0
T CUBE
F V ** 3
G V 3.0 * V ** 2
H V V 6.0 * V
T XEXP
R U VM 1.0 VP -1.0
R W VM 1.0 VP -1.0
R W V -1.0
A EXPW EXP( W )
A UEXPW U * EXPW
F UEXPW
G U EXPW
G W UEXPW
H U W EXPW
H W W UEXPW
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS LUKVLI6
TEMPORARIES
R Z
M ABS
M SIGN
INDIVIDUALS
T L7/3
A Z ABS( GVAR )
F Z**(7.0/3.0)
G 7.0 * SIGN( Z**(4.0/3.0), GVAR ) / 3.0
H 28.0 * Z**(1.0/3.0) / 9.0
ENDATA