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|
*DECK PLQUAD
SUBROUTINE PLQUAD(N0,M1,MAXM,APLUS,BPLUS,PDG,XDROIT,COUT,XOBJ,
> EPS,IMPR,IERR)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Minimize a linear problem with a quadratic constraint using a
* parametric complementarity principle.
* PLQUAD = Linear Programmation with QUADratic constraint
*
*Copyright:
* Copyright (C) 2002 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s):
* A. Hebert and T. Falcon
*
*Parameters: input
* N0 number of control variables.
* M1 number of constraints.
* MAXM first dimension of matrix APLUS.
* APLUS coefficient matrix for the linear constraints.
* BPLUS right hand sides corresponding to the coefficient matrix.
* PDG weights assigned to control variables in the quadratic
* constraint.
* XDROIT quadratic constraint radius squared.
* COUT costs of control variables.
* EPS tolerence used for pivoting.
* IMPR print flag.
*
*Parameters: ouput
* XOBJ control variables.
* IERR return code (=0: normal completion).
*
*-----------------------------------------------------------------------
*
IMPLICIT NONE
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER N0,M1,MAXM,IERR,IMPR
DOUBLE PRECISION BPLUS(M1+1),PDG(N0),XOBJ(N0),EPS,XDROIT,
> APLUS(MAXM,N0),COUT(N0)
*----
* LOCAL VARIABLES
*----
CHARACTER*4 ROW(7)
DOUBLE PRECISION PVAL,POLY0,POLY1,POLY2,XVALIR,X,OBJ,DISCRI,
> XROOT1,XROOT2,XVAL,XTAUU,XVALL,XVALC,OBJLIN
INTEGER N,NP1,NP2,NP3,I,J,K,IS,JS,IROWIS,IR,IROWR,JR,IKIT,II
DOUBLE PRECISION XTAU,XTAUL,UI,XMIN,XVALU
*----
* ALLOCATABLE ARRAYS
*----
INTEGER, ALLOCATABLE, DIMENSION(:) :: IROW,ICOL
DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:) :: U,V,WRK
DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:,:) :: P
*----
* SCRATCH STORAGE ALLOCATION
*----
ALLOCATE(IROW(M1+1),ICOL(M1+2))
ALLOCATE(U(M1+1),V(M1+1))
ALLOCATE(P(M1+1,M1+4),WRK(N0))
*
N = M1 + 1
NP1 = N + 1
NP2 = N + 2
NP3 = N + 3
*----
* STEP 2: SET-UP AND SOLVE THE PARAMETRIC COMPLEMENTARITY PROBLEM.
*----
DO I=1,N
DO J=1,N0
WRK(J) = APLUS(I,J)/PDG(J)
ENDDO
DO K=1,N
PVAL = 0.0D0
DO J=1,N0
PVAL = PVAL + WRK(J)*APLUS(K,J)
ENDDO
P(I,K) = PVAL
ENDDO
ENDDO
*
DO I=1,N
IROW(I) = I
ICOL(I) = -I
P(I,NP1) = 1.0D0
P(I,NP2) = 0.0D0
P(I,NP3) = BPLUS(I)
ENDDO
*
ICOL(NP1) = -NP1
P(N,NP2) = 1.0D0
*
CALL PLLEMK(N,NP3,EPS,IMPR,P,IROW,ICOL,IERR)
*
IF (IERR.GE.1) THEN
WRITE(6,1000) IERR
GO TO 500
ENDIF
*
XTAU = 0.0
XTAUL = 0.0
OBJLIN = BPLUS(N)
*----
* COMPUTE VECTOR T=(NU,PI)=U+XTAU*V
*----
110 POLY0 = 0.0D0
POLY1 = 0.0D0
POLY2 = 0.0D0
*
DO 120 I=1,N
IR = -IROW(I)
IF (IR.GT.0) THEN
U(IR) = P(I,NP3)
V(IR) = P(I,NP2)
POLY0 = POLY0 - P(I,NP3)*BPLUS(IR)
POLY1 = POLY1 - P(I,NP2)*BPLUS(IR)
ELSE
U(-IR) = 0.0
V(-IR) = 0.0
ENDIF
IF (IR.EQ.N) THEN
POLY1 = POLY1 - P(I,NP3)
POLY2 = (-P(I,NP2))
ENDIF
120 CONTINUE
*
IF (IMPR.GE.3) THEN
DO 121 I=1,N0
XOBJ(I) = 0.0
121 CONTINUE
*
DO 123 I=1,N
UI = U(I) + XTAUL*V(I)
IF (UI.EQ.0.0) GO TO 123
DO 122 J=1,N0
XOBJ(J) = XOBJ(J) - UI*APLUS(I,J)/PDG(J)
122 CONTINUE
123 CONTINUE
*
X = 0.0D0
OBJ = 0.0D0
DO 126 J=1,N0
X = X + PDG(J)*XOBJ(J)*XOBJ(J)
OBJ = OBJ + XOBJ(J)*COUT(J)
126 CONTINUE
WRITE(6,2000) OBJ,POLY0,X,POLY1,XTAUL,POLY2,(XOBJ(J),J=1,N0)
ENDIF
IF ((XTAU.EQ.0.0).AND.(POLY0.LE.XDROIT)) GO TO 230
*----
* STEP 3
*----
DO 130 I=1,N
IF(P(I,NP2).LT.-EPS) GO TO 140
130 CONTINUE
GO TO 215
*----
* STEP 4
*----
140 XTAUU = 1.0E+25
*
IR = 0
DO 150 K=I,N
IF(P(K,NP2).GE.-EPS) GO TO 150
XVAL = -P(K,NP3)/P(K,NP2)
IF(XVAL.GT.XTAUU) GO TO 150
XTAUU = XVAL
IR = K
150 CONTINUE
*
XVALU = (POLY2*XTAUU + POLY1)*XTAUU + POLY0
*----
* STEP 5
*----
IF(XVALU.LE.XDROIT) GO TO 215
IROWR = IABS(IROW(IR))
JR=0
DO 160 K=1,NP1
IF(IABS(ICOL(K)).EQ.IROWR) THEN
JR=K
GO TO 170
ENDIF
160 CONTINUE
IERR = 5
GO TO 500
*
170 XTAUL = XTAUU
XVALL = XVALU
IF(P(IR,JR).LE.EPS) GO TO 180
CALL PLPIVT(N,NP3,IR,JR,P,IROW,ICOL)
GO TO 110
*
180 XMIN=1.0E+25
*
XVALIR = P(IR,NP3)/P(IR,NP2)
*
DO 190 I=1,N
IF(P(I,JR).GE.-EPS) GO TO 190
XVAL = -1.0D0/P(I,JR)*(P(I,NP3) - P(I,NP2)*XVALIR)
IF(XVAL.GE.XMIN) GO TO 190
XMIN = XVAL
IS = I
190 CONTINUE
*
IF (XMIN.EQ.1.0E+25) THEN
IERR = 6
GO TO 500
ENDIF
*
IROWIS=IABS(IROW(IS))
DO 200 JS=1,N
IF(IABS(ICOL(JS)).EQ.IROWIS) GO TO 210
200 CONTINUE
*
210 CALL PLPIVT(N,NP3,IR,JS,P,IROW,ICOL)
CALL PLPIVT(N,NP3,IS,JR,P,IROW,ICOL)
GO TO 110
*----
* STEP 6
*----
215 IKIT = 0
*
216 XTAU = (XTAUL + XTAUU)/2.0
IKIT = IKIT + 1
IF (IKIT.GT.50) GOTO 217
XVALC = ((POLY2*XTAU + POLY1)*XTAU + POLY0)/XDROIT
IF (IMPR.GE.3) THEN
WRITE(6,5000) XTAUL,XTAUU,XTAU,POLY0,POLY1,POLY2,XDROIT,XVALC
ENDIF
IF (XVALC.GT.1.0) GO TO 220
IF (XVALC.GE.0.99999) GO TO 230
XTAUU = XTAU
GO TO 216
220 XTAUL = XTAU
GO TO 216
*----
* STEP 6
*----
217 XTAU = (XTAUL + XTAUU)/2.0
XVALC = ((POLY2*XTAU + POLY1)*XTAU + POLY0)/XDROIT
IF (IMPR.GE.3) THEN
WRITE(6,5000) XTAUL,XTAUU,XTAU,POLY0,POLY1,POLY2,XDROIT,XVALC
ENDIF
*
IF (POLY0.EQ.0.0) THEN
IF (POLY1.EQ.0.0) THEN
IF (POLY2.EQ.0.0) THEN
WRITE(6,6000) POLY0,POLY1,POLY2,XDROIT
IERR = 7
GO TO 500
ELSE
IF (POLY2.LT.0.0) THEN
WRITE(6,6000) POLY0,POLY1,POLY2,XDROIT
IERR = 7
GO TO 500
ENDIF
XTAU = SQRT(XDROIT/POLY2)
ENDIF
ELSE IF (POLY2.EQ.0.0) THEN
XTAU = XDROIT/POLY1
ELSE
DISCRI = POLY1*POLY1 + 4.*POLY2*XDROIT
IF (DISCRI.LT.0.0) THEN
WRITE(6,6000) POLY0,POLY1,POLY2,XDROIT
IERR = 7
GO TO 500
ENDIF
XROOT1 = -POLY1 + SQRT(DISCRI)
XROOT2 = -POLY1 - SQRT(DISCRI)
XTAU = MAX(XROOT1,XROOT2)
IF (XTAU.LE.0.0) THEN
WRITE(6,6000) POLY0,POLY1,POLY2,XDROIT
IERR = 7
GO TO 500
ENDIF
XTAU = XTAU/(2.*POLY2)
ENDIF
ELSE IF (POLY1.EQ.0.0) THEN
IF (POLY2.EQ.0.0) THEN
IF ((POLY0.LT.(XDROIT-EPS)).OR.(POLY0.GT.XDROIT+EPS)) THEN
WRITE(6,6000) POLY0,POLY1,POLY2,XDROIT
IERR = 7
GO TO 500
ENDIF
ELSE
DISCRI = XDROIT-POLY0
IF (DISCRI.LT.0.0) THEN
WRITE(6,6000) POLY0,POLY1,POLY2,XDROIT
IERR = 7
GO TO 500
ENDIF
XTAU = SQRT(DISCRI/POLY2)
ENDIF
ELSE IF (POLY2.EQ.0.0) THEN
XTAU = (XDROIT-POLY0)/POLY1
ELSE
DISCRI = POLY1*POLY1 - 4.*POLY2*(POLY0-XDROIT)
IF (DISCRI.LT.0.0) THEN
WRITE(6,6000) POLY0,POLY1,POLY2,XDROIT
IERR = 7
GO TO 500
ENDIF
XROOT1 = -POLY1 + SQRT(DISCRI)
XROOT2 = -POLY1 - SQRT(DISCRI)
XTAU = MAX(XROOT1,XROOT2)
IF (XTAU.LE.0.0) THEN
WRITE(6,6000) POLY0,POLY1,POLY2,XDROIT
IERR = 7
GO TO 500
ENDIF
XTAU = XTAU/(2.*POLY2)
ENDIF
*
IF (IMPR.GE.3) THEN
WRITE(6,5000) XTAUL,XTAUU,XTAU,POLY0,POLY1,POLY2,XDROIT,XVALC
ENDIF
*
IF (ABS(XTAU).GT.XTAUU) THEN
XTAU = XTAUU
ENDIF
*----
* END OF THE ALGORITHM. COMPUTE THE CONTROL VARIABLES.
*----
230 XVALC=(POLY2*XTAU+POLY1)*XTAU+POLY0
*
IF ((IMPR.GE.3).AND.(XVALC.NE.1.0)) THEN
WRITE(6,5000) XTAUL,XTAUU,XTAU,POLY0,POLY1,POLY2,XDROIT,XVALC
ENDIF
*
IF (IMPR.GE.2) THEN
WRITE(6,3000) XTAU,XVALC
DO 255 I=1,N,7
II = MIN0(I+6,N)
DO 250 J=I,II
IF (IROW(J).LT.0) THEN
WRITE (ROW(J-I+1),'(1HX,I3.3)') (-IROW(J))
ELSE
WRITE (ROW(J-I+1),'(1HY,I3.3)') IROW(J)
ENDIF
*
250 CONTINUE
WRITE(6,4000) (ROW(J-I+1),P(J,NP3)+XTAU*P(J,NP2),J=I,II)
255 CONTINUE
ENDIF
IERR = 0
*
XOBJ(:N0)=0.0D0
DO 280 I=1,N
UI = U(I) + XTAU*V(I)
IF (UI.EQ.0.0) GO TO 280
DO 270 J=1,N0
XOBJ(J) = XOBJ(J) - UI*APLUS(I,J)/PDG(J)
270 CONTINUE
280 CONTINUE
*----
* SCRATCH STORAGE DEALLOCATION
*----
500 DEALLOCATE(WRK,P)
DEALLOCATE(V,U)
DEALLOCATE(ICOL,IROW)
RETURN
*
1000 FORMAT(//,5X,'PLQUAD: FAILURE OF THE PARAMETRIC LINEAR COMPLEME',
> 'NTARITY SOLUTION (IERR=',I5,').')
2000 FORMAT(//,5X,'SOLUTION AFTER PIVOTING : ',
> /,5X,'OBJECTIVE FUNCTION = ',1P,E12.5,
> /,5X,'POLY0 = ',1P,E12.5,
> /,5X,'QUADRATIC CONSTRAINT = ',1P,E12.5,
> /,5X,'POLY1 = ',1P,E12.5,
> /,5X,'XTAU PARAMETER = ',1P,E12.5,
> /,5X,'POLY2 = ',1P,E12.5,
> /,5X,'CONTROL VARIABLES = ',/,(5X,1P,10E12.4))
3000 FORMAT(//,5X,'SOLUTION OF THE PARAMETRIC LINEAR COMPLEMENTARITY',
> ' PROBLEM :','*** X: KUHN-TUCKER MULTIPLIERS ;',
> 5X,'*** Y: SLACK VARIABLES ',/,
> /,5X,'TAU = ',1P,E12.5,
> /,5X,'QUADRATIC CONSTRAINT = ',1P,E12.5,/)
4000 FORMAT(7(1X,A4,'=',E12.5),/)
5000 FORMAT( 8X,'XTAUL',7X,'XTAUU',7X,'XTAU ',7X,
> 'POLY0',7X,'POLY1',7X,'POLY2',7X,
> 'XDROIT',6X,'XVALC',/,
> 5X,1P,8E12.5)
6000 FORMAT( 8X,'POLY0',7X,'POLY1',7X,'POLY2',7X,
> 'XDROIT'/5X,1P,4E12.5)
END
|
