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KSIP.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME KSIP
* Problem :
* *********
* Source: problem from Kortanek and No
* The problem is really a semi-infinite QP
* to appear in SIAM J. Optimization.
* The structure is the following :
* min "Sum"{ Xj^2/(2j) + Xj/j ; j=1,...,n } subject to
* "Sum"{ t^(j-1)*Xj } ; j=1,...,n >= b(t) for all t in [0 1].
* Four examples are considered for n = 20, corresponding to the RHS
* function, b(t) : sin(t), 1/(2-t), exp(t), and tan(t).
* The interval [0 1] is dicretized via steps of 1/1000
* SIF input: A.R. Conn, May 1993
* classification QLR2-AN-20-1001
* some useful parameters, including N, the number of variables.
IE N 20
IE M 1000
IA MP1 M 1
RI MR M
IE 1 1
IE 2 2
VARIABLES
DO J 1 N
X X(J)
ND
GROUPS
XG CON(1) X(1) 1.0
DO J 1 N
RI JR J
RA JM1 JR -1.0
RD JINV JR 1.0
ZN OBJ X(J) JINV
DO I 2 MP1
RI IR I
RA IRM1 IR -1.0
R/ T IRM1 MR
R( LOGT LOG T
R* PROD LOGT JM1
R( FACT EXP PROD
ZG CON(I) X(J) FACT
ND
CONSTANTS
DO I 1 MP1
RI IR I
RA IRM1 IR -1.0
R/ T IRM1 MR
R( RHS SIN T
*RM MT T -1.0
*RA TOMT MT 2.0
*RD RHS TOMT 1.0
*R( RHS EXP T
*R( RHS TAN T
Z KSIP CON(I) RHS
ND
BOUNDS
FR KSIP 'DEFAULT'
START POINT
XV KSIP 'DEFAULT' 2.0
ELEMENT TYPE
EV PSQ V1
EP PSQ P
ELEMENT USES
DO J 1 N
XT E(J) PSQ
ZV E(J) V1 X(J)
RI JR J
RM J2 JR 2.0
RD J2INV J2 1.0
ZP E(J) P J2INV
ND
GROUP USES
DO J 1 N
XE OBJ E(J)
ND
OBJECT BOUND
* Solution
*LO SOLTN 0.57579024357147
*LO SOLTN 0.83698795482016
*LO SOLTN 2.51159511773383
*LO SOLTN 0.76079933215965
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS KSIP
INDIVIDUALS
T PSQ
F P * V1**2
G V1 2.0 * P * V1
H V1 V1 2.0 * P
ENDATA