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FERRISDC.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME FERRISDC
* Problem :
* *********
* A QP suggested by Michael Ferris
* from data classification
* SIF input: Nick Gould, November 2001.
* classification QLR2-AN-V-V
*IE n 4 $-PARAMETER
*IE n 100 $-PARAMETER
IE n 200 $-PARAMETER
*IE n 300 $-PARAMETER
*IE k 3 $-PARAMETER
IE k 10 $-PARAMETER
*IE k 20 $-PARAMETER
* Other useful parameters
IE 0 0
IE 1 1
IE 2 2
IE 3 3
RE 12 12.0
RE 24 24.0
RE 240 240.0
IA k-1 k -1
RI k k
RI k-1 k-1
RD -1/k-1 k-1 -1.0
RD -1/k k -1.0
RI n n
RE 1 1.0
RE 2 2.0
R/ 1/12 1 12
R/ 1/24 1 24
R/ 1/240 1 240
RM 7/240 1/240 7.0
R* 2**2 2 2
R* 2**4 2**2 2**2
R* 2**8 2**4 2**4
R* 2**10 2**8 2**2
R* 2**16 2**8 2**8
R* 2**26 2**16 2**10
R/ 2**-26 1 2**26
R* nlambda n 2**-26
R* -1/k-1*nl nlambda -1/k-1
* Initial values and seed value for pseudo random number generator
IE ix 1
IE ax 16807
IE b15 32768
IE b16 65536
IE pp 2147483647
RI pp pp
* param x {J} := ExtUniform(1)
DO j 1 n
* generate a pseudo random number
* xhi=ix/b16
I/ xhi ix b16
* xalo=(ix-xhi*b16)*ax
I* xalo xhi b16
I- xalo ix xalo
I* xalo xalo ax
* leftlo=xalo/b16
I/ leftlo xalo b16
* fhi=xhi*ax+leftlo
I* fhi xhi ax
I+ fhi fhi leftlo
* kk=fhi/b15
I/ kk fhi b15
* ix=(((xalo-leftlo*b16)-pp)+(fhi-kk*b15)*b16)+kk
I* dum leftlo b16
I- dum xalo dum
I- ix dum pp
I* dum kk b15
I- dum fhi dum
I* dum dum b16
I+ ix ix dum
I+ ix ix kk
* if (ix.lt.0) ix=ix+pp
* this is how to write if(a>=0) then ... else ... endif !!
* start by finding c = min(a,0)
* if the value is integer, convert to real
RI a ix
* set a <- - a and b to 0
RM a a -1.0
RE b 0.0
* now add |a| + 2 to both
R( absa ABS a
R( absb ABS b
R+ absa+b absa absb
RA absa+b+2 absa+b 2.0
R+ a a absa+b+2
R+ b b absa+b+2
* only one of [a/b] and [b/a] is nonzero (unless a=0)
R/ a/b a b
R/ b/a b a
IR a/b a/b
IR b/a b/a
RI a/b a/b
RI b/a b/a
* form max(a,b) = (a.[a/b] + b.[b/a]) / ([a/b] + [b/a])
R+ sum a/b b/a
R* a a a/b
R* b b b/a
R+ maxa,b a b
R/ maxa,b maxa,b sum
* subtract |a| + |b| + 2 and negate to find the required minimum, c
R- c absa+b+2 maxa,b
* reset a to its original value
R- a absa+b+2 a
* form f = ( |c| + 2 ) / ( |c| + 1 )
R( absc ABS c
RA absc+1 absc 1.0
RA absc+2 absc 2.0
R/ f absc+2 absc+1
IR f f
* form g = 2 - [f]
IS g f 2
* if ix < 0 ...
DO l 1 g
* ... ix=ix+pp
I+ ix ix pp
OD l
* randp=float(ix)*4.656612875e-10
RI randp ix
A/ X(j) randp pp
OD j
* param r {J} := ExtUniform(1)
DO j 1 n
* generate a pseudo random number
* xhi=ix/b16
I/ xhi ix b16
* xalo=(ix-xhi*b16)*ax
I* xalo xhi b16
I- xalo ix xalo
I* xalo xalo ax
* leftlo=xalo/b16
I/ leftlo xalo b16
* fhi=xhi*ax+leftlo
I* fhi xhi ax
I+ fhi fhi leftlo
* kk=fhi/b15
I/ kk fhi b15
* ix=(((xalo-leftlo*b16)-pp)+(fhi-kk*b15)*b16)+kk
I* dum leftlo b16
I- dum xalo dum
I- ix dum pp
I* dum kk b15
I- dum fhi dum
I* dum dum b16
I+ ix ix dum
I+ ix ix kk
* if (ix.lt.0) ix=ix+pp
* this is how to write if(a>=0) then ... else ... endif !!
* start by finding c = min(a,0)
* if the value is integer, convert to real
RI a ix
* set a <- - a and b to 0
RM a a -1.0
RE b 0.0
* now add |a| + 2 to both
R( absa ABS a
R( absb ABS b
R+ absa+b absa absb
RA absa+b+2 absa+b 2.0
R+ a a absa+b+2
R+ b b absa+b+2
* only one of [a/b] and [b/a] is nonzero (unless a=0)
R/ a/b a b
R/ b/a b a
IR a/b a/b
IR b/a b/a
RI a/b a/b
RI b/a b/a
* form max(a,b) = (a.[a/b] + b.[b/a]) / ([a/b] + [b/a])
R+ sum a/b b/a
R* a a a/b
R* b b b/a
R+ maxa,b a b
R/ maxa,b maxa,b sum
* subtract |a| + |b| + 2 and negate to find the required minimum, c
R- c absa+b+2 maxa,b
* reset a to its original value
R- a absa+b+2 a
* form f = ( |c| + 2 ) / ( |c| + 1 )
R( absc ABS c
RA absc+1 absc 1.0
RA absc+2 absc 2.0
R/ f absc+2 absc+1
IR f f
* form g = 2 - [f]
IS g f 2
* if ix < 0 ...
DO l 1 g
* ... ix=ix+pp
I+ ix ix pp
OD l
* randp=float(ix)*4.656612875e-10
RI randp ix
A/ R(j) randp pp
OD j
* param p {j = 1, ... , n, i = 1, ..., k} >= 0, <= 1, :=
* if i = 1 then .97*exp(-3*x[j])
* else if i = 3 then exp(-2.5*(x[j]-1.2)**2)
* else 1 - p[j,1] - p[j,3];
DO j 1 n
AM arg X(j) -3.0
R( arg EXP arg
AM P(j,1) arg 0.97
AA arg X(j) -1.2
R* arg arg arg
RM arg arg -2.5
A( P(j,3) EXP arg
A- arg 1 P(j,1)
A- P(j,2) arg P(j,3)
ND
*param y {j = 1, ... , n} :=
* if r[j] <= p[j,1] then 1
* else if r[j] <= 1 - p[j,3] then 2
* else 3;
DO j 1 n
* if a = p[j,1] - r[j] >= 0 ...
A- a P(j,1) R(j)
* this is how to write if(a>=0) then ... else ... endif !!
* start by finding c = min(a,0)
* set a <- - a and b to 0
RM a a -1.0
RE b 0.0
* now add |a| + 2 to both
R( absa ABS a
R( absb ABS b
R+ absa+b absa absb
RA absa+b+2 absa+b 2.0
R+ a a absa+b+2
R+ b b absa+b+2
* only one of [a/b] and [b/a] is nonzero (unless a=0)
R/ a/b a b
R/ b/a b a
IR a/b a/b
IR b/a b/a
RI a/b a/b
RI b/a b/a
* form max(a,b) = (a.[a/b] + b.[b/a]) / ([a/b] + [b/a])
R+ sum a/b b/a
R* a a a/b
R* b b b/a
R+ maxa,b a b
R/ maxa,b maxa,b sum
* subtract |a| + |b| + 2 and negate to find the required minimum, c
R- c absa+b+2 maxa,b
* reset a to its original value
R- a absa+b+2 a
* form f = ( |c| + 2 ) / ( |c| + 1 )
R( absc ABS c
RA absc+1 absc 1.0
RA absc+2 absc 2.0
R/ f absc+2 absc+1
IR f f
* form g = 2 - [f]
IS g f 2
* if a = p[j,1] - r[j] >= 0 ...
DO l1 g 0
* ... set y(j) = 1
AE y(j) 1.0
OD l1
* if a = p[j,1] - r[j] < 0 ...
DO l1 1 g
* then if r[j] <= 1 - p[j,3] ...
* if a = 1 - p[j,3] - r[j] >= 0 ...
A- a 1 P(j,3)
A- a a R(j)
* this is how to write if(a>=0) then ... else ... endif !!
* start by finding c = min(a,0)
* set a <- - a and b to 0
RM a a -1.0
RE b 0.0
* now add |a| + 2 to both
R( absa ABS a
R( absb ABS b
R+ absa+b absa absb
RA absa+b+2 absa+b 2.0
R+ a a absa+b+2
R+ b b absa+b+2
* only one of [a/b] and [b/a] is nonzero (unless a=0)
R/ a/b a b
R/ b/a b a
IR a/b a/b
IR b/a b/a
RI a/b a/b
RI b/a b/a
* form max(a,b) = (a.[a/b] + b.[b/a]) / ([a/b] + [b/a])
R+ sum a/b b/a
R* a a a/b
R* b b b/a
R+ maxa,b a b
R/ maxa,b maxa,b sum
* subtract |a| + |b| + 2 and negate to find the required minimum, c
R- c absa+b+2 maxa,b
* reset a to its original value
R- a absa+b+2 a
* form f = ( |c| + 2 ) / ( |c| + 1 )
R( absc ABS c
RA absc+1 absc 1.0
RA absc+2 absc 2.0
R/ f absc+2 absc+1
IR f f
* form g = 2 - [f]
IS g f 2
* else if r[j] <= 1 - p[j,3] ...
* if c = 0
DO l2 g 0
* ... set y(j) = 2
AE y(j) 2.0
OD l2
* else ...
DO l2 1 g
* ... set y(j) = 3
AE y(j) 3.0
OD l2
OD l1
OD j
* param Y {i = 1, ..., k, j = 1, ... , n} :=
* (if y[j] = i then 1
* else -1/(k-1))*nlambda;
DO j 1 n
A= yj y(j)
IR yj yj
DO i 1 k
* if c = Y(j) - i = 0 ...
I- c yj i
* this is how to write if(c=0) then ... else ... endif !!
* if c is integer, convert to real
RI c c
* form f = ( |c| + 2 ) / ( |c| + 1 )
R( absc ABS c
RA absc+1 absc 1.0
RA absc+2 absc 2.0
R/ f absc+2 absc+1
IR f f
* form g = 2 - [f]
IS g f 2
* (if y[j] = i ...
DO l g 0
A= Y(i,j) nlambda
OD l
* else ...
DO l 1 g
A= Y(i,j) -1/k-1*nl
OD l
OD i
OD j
* coefficients of the Hessian
DO i 1 n
AA di X(i) -0.5
A* di2 di di
A- di2 di2 1/12
DO j i n
* b {i = 1, ... , n, j = 1, ... , n} := abs(x[i]-x[j]);
A- Xi-Xj X(i) X(j)
R( bij ABS Xi-Xj
* K {i = 1, ... , n, j = 1, ... , n} :=
* (x[i]-0.5)*(x[j]-0.5)
* + ( (x[i]-0.5)**2-1/12 ) * ( (x[j]-0.5)**2-1/12 ) / 4
* - ( (b[i,j]-0.5)**4 - ( (b[i,j]-0.5)**2 ) / 2 + 7/240 ) / 24;
AA dj X(j) -0.5
A* dj2 dj dj
A- dj2 dj2 1/12
RA c bij -0.5
R* c2 c c
R* c4 c2 c2
RM c2 c2 -0.5
R+ arg 7/240 c2
R+ arg arg c4
R* arg arg 1/24
R* dij di dj
*A= 1-(i,j) dij
R* dij2 di2 dj2
RM dij2 dij2 0.25
*A= 2-(i,j) dij2
*A= 3-(i,j) arg
R- arg dij2 arg
A+ K(i,j) dij arg
ND
VARIABLES
DO i 1 k
DO j 1 n
X A(i,j)
ND
DO i 1 n
X W(i)
ND
GROUPS
* linear part of the objective
* min 1/2 sum_i=1^k a(i,.) T K a(i,.) - 1/2k w^T K w
* a,w + sum_i=1^k y(i,.) T a(i,.)
DO j 1 n
DO i 1 k
ZN OBJ A(i,j) Y(i,j)
ND
* true linear constraints
* sum_j=1^n a(i,j) - 1/k sum_j=1^n w(j) = 0 ( i = 1, ... , k )
DO i 1 k
DO j 1 n
XE C(i) A(i,j) 1.0
ZE C(i) W(j) -1/k
ND
* artificial linear constraints
* sum_i=1^k a(i,j) - w(j) = 0 ( j = 1, .... , n )
DO j 1 n
XE A(j) W(j) -1.0
DO i 1 k
XE A(j) A(i,j) 1.0
ND
BOUNDS
LO FERRISDC 'DEFAULT' 0.0
UP FERRISDC 'DEFAULT' 1.0
DO i 1 n
XR FERRISDC W(i)
ND
* param L {i = 1, ..., k, j = 1, ... , n} binary :=
* if y[j] = i then 0
* else 1;
DO j 1 n
A= yj y(j)
IR yj yj
DO i 1 k
* if c = Y(j) - i = 0 ...
I- c yj i
* this is how to write if(c=0) then ... else ... endif !!
* if c is integer, convert to real
RI c c
* form f = ( |c| + 2 ) / ( |c| + 1 )
R( absc ABS c
RA absc+1 absc 1.0
RA absc+2 absc 2.0
R/ f absc+2 absc+1
IR f f
* form g = 2 - [f]
IS g f 2
* (if y[j] = i ...
DO l g 0
XX FERRISDC A(i,j) 0.0
OD l
OD i
OD j
QUADRATIC
* quadratic part of the objective
* min 1/2 sum_i=1^k a(i,.) T K a(i,.) - 1/2k w^T K w
* a,w + sum_i=1^k y(i,.) T a(i,.)
DO i 1 k
DO l 1 n
DO j 1 l
Z A(i,j) A(i,l) K(j,l)
ND
DO l 1 n
DO j 1 l
A* coef -1/k K(j,l)
Z W(j) W(l) coef
ND
OBJECT BOUND
* Solution
*XL SOLUTION -1.131846D+2 $ nlambda = 1.5625
*XL SOLUTION -8.032841E-5 $ nlambda = 1.4901E-06
ENDATA