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*DECK PLLA
SUBROUTINE PLLA(IPOPT,N0,M0,APLUS,PDG,BPLUS,INPLUS,XDROIT,FCOST,
> GF,XOBJ,IMPR,EPSIM,NCST,GRAD,CONTR,INEGAL,IERR)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Solves the quasi-linear problem using the augmented Lagrangian.
* PLLA = Linear Programmation Augmented Lagrangian
*
*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): R. Chambon
*
*Parameters: input/ouput
* IPOPT pointer to the L_OPTIMIZE object.
* N0 number of control variables.
* M0 number of constraints.
* APLUS coefficient matrix for the linear constraints.
* PDG weights assigned to control variables in the quadratic
* constraint.
* BPLUS right hand sides corresponding to the coefficient matrix.
* INPLUS constraint relations (=-1 for .GE.; =0 for .EQ.; =1 for .LE.).
* XDROIT quadratic constraint radius squared.
* FCOST costs of control variables.
* GF objective function.
* XOBJ control variables.
* IMPR print flag.
* EPSIM tolerence used for inner linear SIMPLEX calculation.
* NCST number of constraints.
* GRAD linearized gradients (GRAD(:,1) are control variable costs
* and GRAD(:,2:NCST+1) are linear constraint coefficients).
* CONTR constraint right hand sides.
* INEGAL constraint relations (=-1 for .GE.; =0 for .EQ.; =1 for .LE.).
*
*Parameters: ouput
* IERR return code (=0: normal completion).
*
*-----------------------------------------------------------------------
*
USE GANLIB
IMPLICIT NONE
*----
* SUBROUTINE ARGUMENTS
*----
TYPE(C_PTR) IPOPT
INTEGER N0,M0,INPLUS(M0+1),IMPR,NCST,INEGAL(NCST),IERR
DOUBLE PRECISION PDG(N0),BPLUS(M0+2),XDROIT,XOBJ(N0),EPSIM,
> GRAD(N0,NCST+1),CONTR(NCST),APLUS(M0+2,M0+N0+1),GF(N0),FCOST
*----
* LOCAL VARIABLES
*----
INTEGER ITERMX,LENGT,ITYP,I,J,K,ITER,NPM,M0B
PARAMETER (ITERMX=10)
LOGICAL LCST(NCST),LCST2(NCST),LTST
DOUBLE PRECISION LACOST,NORM,CRIT,LA0E
INTEGER, ALLOCATABLE, DIMENSION(:) :: INPL2
DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:) :: LAFAC,CSTWGT,B2,
> CONTR2,LAGF
DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:,:) :: APLUS2
*----
* SCRATCH STORAGE ALLOCATION
*----
ALLOCATE(INPL2(M0-NCST+1))
ALLOCATE(LAFAC(NCST),CSTWGT(NCST),B2(M0-NCST+2),CONTR2(NCST))
ALLOCATE(LAGF(N0),APLUS2(M0-NCST+1,N0+M0-NCST))
*----
* STEP 0: INITIALIZATION
* NPM: SIZE OF THE LINEARIZED SYSTEM.
* M0B: NUMBER OF LINEARIZED CONSTRAINTS FOR THE LA ALGORITHM.
* CORRESPONDS TO THE NUMBER OF POSSIBLY ACTIVE BOUNDS.
*----
NPM=(M0+1)+N0
M0B=M0-NCST
IF(NCST.GT.0) THEN
CALL LCMLEN(IPOPT,'F-LA-MULT',LENGT,ITYP)
IF(LENGT.EQ.0) THEN
CALL XABORT('PLLA: LAGRANGIAN FACTORS NON INITIALIZED')
ELSEIF(LENGT.EQ.NCST) THEN
CALL LCMGET(IPOPT,'F-LA-MULT',LAFAC)
ELSE
CALL XABORT('PLLA: WRONG NUMBER OF LA COEFFICIENTS')
ENDIF
CALL LCMLEN(IPOPT,'CST-WEIGHT',LENGT,ITYP)
IF(LENGT.EQ.0) THEN
CALL XABORT('PLLA: CONSTRAINTS PENALTIES NON INITIALIZED')
ELSEIF(LENGT.EQ.NCST) THEN
CALL LCMGET(IPOPT,'CST-WEIGHT',CSTWGT)
ELSE
CALL XABORT('PLLA: WRONG NUMBER OF CONSTRAINT WEIGHTS')
ENDIF
DO 10 J=1,NCST
CONTR2(J)=-CONTR(J)
10 CONTINUE
LCST2(:NCST)=.TRUE.
LCST(:NCST)=.TRUE.
ENDIF
XOBJ(:N0)=0.0D0
*----
* INTERNAL ITERATIONS FOR THE LINEAR PROBLEM
*----
ITER=0
99 ITER=ITER+1
LTST=.TRUE.
*----
* STEP 1: LA FUNCTION EVALUATION
*----
DO 110 J=1,NCST
IF(INEGAL(J).NE.0) THEN
CRIT=CONTR2(J)
DO 100 I=1,N0
CRIT=CRIT+GRAD(I,J+1)*XOBJ(I)
100 CONTINUE
CRIT=CSTWGT(J)*INEGAL(J)*CRIT+LAFAC(J)
LCST(J)=(CRIT.LE.0.0)
ENDIF
110 CONTINUE
DO 150 I=1,N0
LAGF(I)=GF(I)
DO 140 J=1,NCST
IF(INEGAL(J).EQ.0) THEN
LAGF(I)=LAGF(I)+GRAD(I,J+1)*(LAFAC(J)+CSTWGT(J)*CONTR2(J))
ELSEIF(.NOT.LCST(J)) THEN
LAGF(I)=LAGF(I)+INEGAL(J)*GRAD(I,J+1)
1 *(CSTWGT(J)*INEGAL(J)*CONTR2(J)+2*LAFAC(J))
ENDIF
140 CONTINUE
150 CONTINUE
LACOST=FCOST
DO 160 J=1,NCST
IF(INEGAL(J).EQ.0) THEN
LACOST=LACOST+(LAFAC(J)+CSTWGT(J)/2.0*CONTR2(J))*CONTR2(J)
ELSEIF(.NOT.LCST(J)) THEN
LACOST=LACOST+INEGAL(J)*CONTR2(J)*2.0*LAFAC(J)
1 +CSTWGT(J)/2.0*CONTR2(J)**2
ELSE
LACOST=LACOST-3.0*LAFAC(J)**2/2.0/CSTWGT(J)
ENDIF
160 CONTINUE
IF(ITER.EQ.1) LA0E=LACOST
IF(IMPR.GE.3) THEN
WRITE(6,*) 'GF',(GF(I),I=1,N0)
WRITE(6,*) 'LAGF',(LAGF(I),I=1,N0)
WRITE(6,*) 'PDG',(PDG(I),I=1,N0)
WRITE(6,*) 'LACOST',LACOST,'M0B',M0B,'XDROIT',XDROIT
ENDIF
*----
* STEP 2: SOLUTION
* k,l
* compute DX
* case 1
* If there is no constraints for the LA problem (M0B=0),
* then the solution is obvious: on the hypersphere(radius XDROIT)
* in the direction LAGF
*----
IF(M0B.EQ.0) THEN
*
NORM=0.0
DO 200 I=1,N0
NORM=NORM+LAGF(I)**2/PDG(I)
200 CONTINUE
NORM=NORM**0.5
*
IF(NORM.EQ.0.0) THEN
XOBJ(:N0)=0.0D0
ELSE
DO 210 I=1,N0
XOBJ(I)=-XDROIT**0.5*LAGF(I)/PDG(I)/NORM
210 CONTINUE
ENDIF
*----
* CASE 2
* SOLUTION WITH THE LEMKE METHOD
*----
ELSE
*
DO 260 K=1,M0B
DO 250 I=1,N0
APLUS2(K,I)=APLUS(NCST+K,I)
250 CONTINUE
B2(K)=BPLUS(NCST+K)
INPL2(K)=INPLUS(NCST+K)
260 CONTINUE
DO 270 I=1,N0
APLUS2(M0B+1,I) = 0.0D0
270 CONTINUE
BPLUS(M0B+1) = 0.0
INPL2(M0B+1) = 0
*
CALL PLMAP2(N0,M0B,APLUS2,PDG,B2,INPL2,XDROIT,LAGF,LACOST,XOBJ,2,
> EPSIM,IMPR,IERR)
*
ENDIF
DO 410 J=1,NCST
IF(INEGAL(J).NE.0) THEN
CRIT=CONTR2(J)
DO 400 I=1,N0
CRIT=CRIT+GRAD(I,J+1)*XOBJ(I)
400 CONTINUE
CRIT=CSTWGT(J)*INEGAL(J)*CRIT+LAFAC(J)
LCST2(J)=(CRIT.LE.0.0)
ENDIF
410 CONTINUE
IF((IMPR.GE.2).AND.(NCST.GT.0)) THEN
WRITE(6,*) (LCST(J),J=1,NCST)
WRITE(6,*) (LCST2(J),J=1,NCST)
ENDIF
DO 420 J=1,NCST
LTST=LTST.AND.(LCST(J).EQV.LCST2(J))
420 CONTINUE
IF((.NOT.LTST) .AND.(ITER.LE.ITERMX)) GO TO 99
*----
* k,l
* STEP 3: SAVE L
* a
*----
CALL LCMSIX(IPOPT,'OLD-VALUE',1)
CALL LCMPUT(IPOPT,'F-LA-EVAL',1,4,LA0E)
IF(IMPR.GE.1) WRITE(6,*) 'LAGF',(LAGF(I),I=1,N0)
CALL LCMPUT(IPOPT,'DF-LA-PENAL',N0,4,LAGF)
CALL LCMSIX(IPOPT,' ',0)
*
IF(IMPR.GE.1) WRITE(6,*) 'Dvar',(XOBJ(I),I=1,N0)
*----
* SCRATCH STORAGE DEALLOCATION
*----
DEALLOCATE(APLUS2,LAGF)
DEALLOCATE(CONTR2,B2,CSTWGT,LAFAC)
DEALLOCATE(INPL2)
RETURN
END
|
