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MADSSCHJ.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME MADSSCHJ
* Problem :
* *********
* A nonlinear minmax problem with variable dimension.
* The Jacobian of the constraints is dense.
* Source:
* K. Madsen and H. Schjaer-Jacobsen,
* "Linearly Constrained Minmax Optimization",
* Mathematical Programming 14, pp. 208-223, 1978.
* SIF input: Ph. Toint, August 1993.
* classification LQR2-AN-V-V
* N is the number of variables - 1, and must be even and at least 4.
* The number of inequality constraints is 2*N - 2.
*IE N 4 $-PARAMETER n= 5, m= 6
*IE N 10 $-PARAMETER n= 11, m= 18 original value
*IE N 20 $-PARAMETER n= 21, m= 38
*IE N 30 $-PARAMETER n= 31, m= 58
*IE N 40 $-PARAMETER n= 41, m= 78
*IE N 50 $-PARAMETER n= 51, m= 98
*IE N 60 $-PARAMETER n= 61, m=118
*IE N 70 $-PARAMETER n= 71, m=138
*IE N 80 $-PARAMETER n= 81, m=158
*IE N 90 $-PARAMETER n= 91, m=178
*IE N 100 $-PARAMETER n=101, m=198
IE N 200 $-PARAMETER n=201, m=398
* Constants
IE 1 1
IE 2 2
IE 3 3
IE 4 4
IA N-1 N -1
I+ 2N N N
IA M 2N -2
IA M-1 M -1
VARIABLES
DO I 1 N
X X(I)
OD I
Z
GROUPS
* Objective
XN OBJ Z 1.0
* First constraint
XG C1 Z 1.0
DO I 2 N
XG C1 X(I) -1.0
OD I
* Second constraint
XG C2 Z 1.0 X1 -1.0
DO I 3 N
XG C2 X(I) -1.0
OD I
* Third constraint
XG C3 Z 1.0 X1 -1.0
DO I 3 N
XG C3 X(I) -1.0
OD I
* Subsequent intermediate constraints, by blocks of 2
DO K 4 M-1
DI K 2
IA K+1 K 1
IA K+2 K 2
I/ J K+2 2
IA J-1 J -1
IA J+1 J 1
XG C(K) Z 1.0
XG C(K+1) Z 1.0
DO I 1 J-1
XG C(K) X(I) -1.0
XG C(K+1) X(I) -1.0
OD I
DO I J+1 N
XG C(K) X(I) -1.0
XG C(K+1) X(I) -1.0
OD I
OD K
* Last constraint
XG C(M) Z 1.0
DO I 1 N-1
XG C(M) X(I) -1.0
OD I
CONSTANTS
DO K 1 M
X MADSSCHJ C(K) -1.0
OD K
BOUNDS
FR MADSSCHJ 'DEFAULT'
START POINT
XV MADSSCHJ 'DEFAULT' 10.0
XV MADSSCHJ Z 0.0
ELEMENT TYPE
EV SQ X
ELEMENT USES
DO I 1 N
XT XSQ(I) SQ
ZV XSQ(I) X X(I)
OD I
GROUP USES
XE C(1) XSQ(1) -1.0
XE C(2) XSQ(2) -1.0
XE C(3) XSQ(2) -2.0
DO K 4 M-1
DI K 2
IA K+1 K 1
IA K+2 K 2
I/ J K+2 2
XE C(K) XSQ(J) -1.0
XE C(K+1) XSQ(J) -2.0
OD K
XE C(M) XSQ(N) -1.0
OBJECT BOUND
* Solution
*LO SOLTN(4) -2.6121094144
*LO SOLTN(10) -12.814452425
*LO SOLTN(20) -49.869888156
*LO SOLTN(30) -111.93545559
*LO SOLTN(40) -199.00371592
*LO SOLTN(50) -311.07308068
*LO SOLTN(60) -448.14300524
*LO SOLTN(70) -610.21325256
*LO SOLTN(80) -797.28370289
*LO SOLTN(90) -1009.3542892
*LO SOLTN(100) -1246.4249710
*LO SOLTN(200) -4992.1339031
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS MADSSCHJ
INDIVIDUALS
T SQ
F X * X
G X X + X
H X X 2.0
ENDATA