[u/mrichter/AliRoot.git] / HERWIG / jimmy / divon4 / bndopt.F

*CMZ :          23/08/93  13.30.10  by  Jonathan Butterworth
*-- Author :
      SUBROUTINE BNDOPT (N,XMIN,XMAX,XLOW,XHI,FMIN,FMAX,FLOBD,FUPBD,X,XT
     1EMP,GFREE,PFREE,GACTV,GNEW,AHESS,DELTA,FTOL,GTOL,ETA,ALFMAX,MAXFUN
     2,NFCNT,IFREE,IACTV,IPRINT,IRESLT)
      INTEGER N, MAXFUN, NFCNT, IPRINT, IRESLT
      INTEGER IFREE(N), IACTV(N)
      DOUBLE PRECISION FMIN, FMAX, FLOBD, FUPBD, DELTA, FTOL, GTOL,
     1                 ETA, ALFMAX
      DOUBLE PRECISION XMIN(N), XMAX(N), XLOW(N), XHI(N), X(N),
     1                 XTEMP(N), GFREE(N), PFREE(N), GACTV(N), GNEW(N),
     2                 AHESS(N,N)
      INTEGER I, IBDEL, IBTRUE, IDNEW, II, IIMIN, ILOC, INEW, IPCNT,
     1        ITER, ITEST, J, NACTV, NADIM, NFREE
      LOGICAL LOCAL, NEGMUL, XALTER
      DOUBLE PRECISION  A, ALPHA, ALRAT, B, BTOL, B1, D, DEL, DFUN,
     1 DVDOT, DXNORM, E, EPSMCH, FA, FBD, FBEST, FDIFF,
     2                  FOLD, FRAT, FTEST, FTRUE, FU, FV, FW, FY, FZ,
     3                  GNORM, GTEST1, GTEST2, GTP, GU, OLDF, PE,
     4                  PNORM, QEPS, R, RR, RTEPS, SCXBD, SFTBND, SS,
     5                  STEPMX, T, TOL, U, XBEST, XLAMDA, XNORM, XRAT,
     6                  XV, XW, ZTOL1, ZTOL2
      DATA EPSMCH/2.22D-16/
      SAVE
      RTEPS=SQRT(EPSMCH)
      QEPS=SQRT(RTEPS)
      ZTOL1=ABS(FTOL)
      NADIM=N
      NFCNT=0
      DO 10 I=1,N
      IFREE(I)=0
      IACTV(I)=0
 10   CONTINUE
      IF(IPRINT.LT.0) GOTO 20
      WRITE(6,310)
      WRITE(6,320) (XLOW(I),I=1,N)
      WRITE(6,330) (XHI(I),I=1,N)
 20   DO 300 IIMIN=1,2
      IF(IIMIN.EQ.2) GOTO 30
      CALL DVCOPY(N,XMIN,X)
      FTRUE=FMIN
      FBEST=FTRUE
      FBD=FLOBD
      GOTO 40
 30   CALL DVCOPY(N,XMAX,X)
      FTRUE=FMAX
      FBEST=-FTRUE
      FBD=FUPBD
 40   ITER=0
      GNORM=0.0D+0
      IPCNT=0
      FOLD=FBEST
      LOCAL=.FALSE.
      DO 60 J=1,N
      DO 50 I=1,N
      AHESS(I,J)=0.0D+0
 50   CONTINUE
      AHESS(J,J)=1.0D+0
 60   CONTINUE
      BTOL=QEPS
 70   CALL BNDTST(N,X,XLOW,XHI,BTOL,NFREE,IFREE,NACTV,IACTV,XALTER)
      IF(.NOT.XALTER) GOTO 80
      FTRUE=DFUN(N,X)
      FBEST=FTRUE
      IF(IIMIN.EQ.2) FBEST=-FTRUE
      FOLD=FBEST
 80   IF(IPRINT.LT.0) GOTO 90
      IF(IIMIN.EQ.1) WRITE(6,340) FTRUE
      IF(IIMIN.EQ.2) WRITE(6,350) FTRUE
      IF(LOCAL) WRITE(6,450) NFCNT
      WRITE(6,360) (X(I),I=1,N)
      WRITE(6,370) NFREE,NACTV
      IF(NFREE.GT.0.AND.NFREE.LT.N) WRITE(6,380) (IFREE(I),I=1,NFREE)
      IF(NACTV.GT.0.AND.NACTV.LT.N) WRITE(6,390) (IACTV(I),I=1,NACTV)
 90   FTEST=RTEPS*(1.0D+0+ABS(FBD))
      IF(ABS(FBD-FBEST).LT.FTEST) GOTO 250
      IF(NFREE.EQ.0) GOTO 250
      CALL GRDCMP(N,NFREE,IFREE,X,FTRUE,DELTA,XHI,XTEMP,GFREE)
      NFCNT=NFCNT+NFREE
      IF(IIMIN.EQ.1) GOTO 110
      DO 100 I=1,NFREE
      GFREE(I)=-GFREE(I)
 100  CONTINUE
 110  CALL RLEN(NFREE,GFREE,GNORM)
      IF(GNORM.GT.GTOL.OR.LOCAL) GOTO 120
      IF(IPRINT.GT.0) WRITE(6,440)
      DEL=DELTA
      IF(DELTA.LT.1.0D+0) DEL=SQRT(DELTA)
      ZTOL2=10.0D+0*SQRT(RTEPS*DEL)
      IF(ZTOL2.LT.RTEPS) ZTOL2=RTEPS
      LOCAL=.TRUE.
      CALL LOCSCH(IIMIN,N,NFREE,IFREE,X,FBEST,XLOW,XHI,DEL,ZTOL2,NFCNT,
     1GNEW,FY,XTEMP,FZ,PFREE)
      FTEST=RTEPS*(1.0D+0+ABS(FBEST))
      IF(FZ.GE.FBEST.OR.ABS(FZ-FBEST).LT.FTEST) GOTO 250
      CALL DVCOPY(N,XTEMP,X)
      FBEST=FZ
      FTRUE=FZ
      IF(IIMIN.EQ.2) FTRUE=-FZ
      GOTO 70
 120  ITER=ITER+1
      IF(NFCNT.GT.MAXFUN) GOTO 270
      IF(IPCNT.GE.IPRINT) IPCNT=0
      IPCNT=IPCNT+1
      IF(NFREE.EQ.0) GOTO 250
      CALL LDLSOL(NFREE,NADIM,AHESS,GFREE,PFREE)
      DO 130 I=1,NFREE
      PFREE(I)=-PFREE(I)
 130  CONTINUE
      CALL RLEN(NFREE,PFREE,PNORM)
      PE=PNORM+RTEPS
      CALL FEASMV(N,NFREE,IFREE,X,PFREE,XLOW,XHI,EPSMCH,STEPMX,INEW,IDN
     1EW)
      IF((STEPMX*PE).GT.DELTA) GOTO 140
      CALL ADDBND(N,NFREE,IFREE,NACTV,IACTV,INEW,IDNEW,NADIM,AHESS,XTEM
     1P,GFREE,GNORM)
      ITER=ITER-1
      GOTO 120
 140  GTP=DVDOT(NFREE,GFREE,PFREE)
      XLAMDA=MIN(STEPMX,ALFMAX)
      U=MIN(1.0D+0,XLAMDA)
      FU=FBEST
      GU=GTP
      ILOC=1
      SFTBND=DELTA/PE
      T=RTEPS/PE
      DO 150 I=1,N
      XTEMP(I)=X(I)
 150  CONTINUE
 160  CALL NEWPTQ(RTEPS,T,ETA,SFTBND,XLAMDA,U,FU,GU,XBEST,FBEST,XW,FW,X
     1V,FV,A,FA,B,OLDF,B1,SCXBD,E,D,RR,SS,GTEST1,GTEST2,TOL,ILOC,ITEST)
      IF(ITEST.NE.1) GOTO 180
      R=XBEST+U
      DO 170 I=1,NFREE
      II=IFREE(I)
      XTEMP(II)=X(II)+R*PFREE(I)
 170  CONTINUE
      FU=DFUN(N,XTEMP)
      NFCNT=NFCNT+1
      IF(IIMIN.EQ.2) FU=-FU
      GOTO 160
 180  IF(ITEST.NE.0) GOTO 250
      ALPHA=XBEST
      DO 190 I=1,NFREE
      II=IFREE(I)
      X(II)=X(II)+XBEST*PFREE(I)
 190  CONTINUE
      FTRUE=FBEST
      IF(IIMIN.EQ.2) FTRUE=-FBEST
      IF(IPRINT.LE.0.OR.IPCNT.LT.IPRINT) GOTO 200
      WRITE(6,400) ITER,NFCNT,FBEST
      WRITE(6,360) (X(I),I=1,N)
      WRITE(6,370) NFREE,NACTV
      IF(NFREE.GT.0.AND.NFREE.LT.N) WRITE(6,380) (IFREE(I),I=1,NFREE)
      IF(NACTV.GT.0.AND.NACTV.LT.N) WRITE(6,390) (IACTV(I),I=1,NACTV)
 200  CALL GRDCMP(N,NFREE,IFREE,X,FTRUE,DELTA,XHI,XTEMP,GNEW)
      CALL RLEN(NFREE,GNEW,GNORM)
      IF(IPRINT.GT.0.AND.IPCNT.EQ.IPRINT) WRITE(6,460) GNORM
      IF(IIMIN.EQ.1) GOTO 220
      DO 210 I=1,NFREE
      GNEW(I)=-GNEW(I)
 210  CONTINUE
 220  NFCNT=NFCNT+NFREE
      CALL BFGS(NFREE,NADIM,AHESS,EPSMCH,GFREE,GNEW,PFREE,ALPHA,XTEMP)
      DO 230 I=1,NFREE
      GFREE(I)=GNEW(I)
 230  CONTINUE
      ALRAT=ABS(ALPHA-STEPMX)/STEPMX
      IF(ALRAT.GE.QEPS) GOTO 240
      CALL ADDBND(N,NFREE,IFREE,NACTV,IACTV,INEW,IDNEW,NADIM,AHESS,XTEM
     1P,GFREE,GNORM)
      GOTO 120
 240  FDIFF=FOLD-FBEST
      FRAT=FDIFF/(1.0D+0+ABS(FBEST))
      IF(FTOL.LT.0.0D+0) FRAT=FDIFF/MAX(ABS(FBEST),EPSMCH)
      CALL RLEN(N,X,XNORM)
      DXNORM=ALPHA*PNORM
      XRAT=DXNORM/(1.0D+0+XNORM)
      IF(FTOL.LT.0.0D+0) XRAT=DXNORM/MAX(XNORM,EPSMCH)
      FOLD=FBEST
      IF(FRAT.GT.ZTOL1.OR.XRAT.GT.ZTOL1) GOTO 120
 250  IF(NACTV.EQ.0) GOTO 270
      CALL MULCHK(N,NACTV,IACTV,IIMIN,RTEPS,X,XHI,FTRUE,DELTA,XTEMP,GAC
     1TV,NEGMUL,IBDEL,IBTRUE)
      NFCNT=NFCNT+NACTV
      IF(IPRINT.LE.0.OR.IPCNT.LT.IPRINT) GOTO 260
      WRITE(6,420) ITER,NACTV
      WRITE(6,390) (IACTV(I),I=1,NACTV)
      WRITE(6,430) (GACTV(I),I=1,NACTV)
 260  IF(.NOT.NEGMUL) GOTO 270
      CALL DELBND(N,NACTV,IACTV,NFREE,IFREE,IBDEL,IBTRUE,GACTV,NADIM,AH
     1ESS,GFREE,GNORM)
      GOTO 120
 270  IF(IPRINT.LT.0) GOTO 280
      WRITE(6,410) ITER,NFCNT,FTRUE
      WRITE(6,360) (X(I),I=1,N)
      WRITE(6,370) NFREE,NACTV
      IF(NFREE.GT.0.AND.NFREE.LT.N) WRITE(6,380) (IFREE(I),I=1,NFREE)
      IF(NACTV.GT.0.AND.NACTV.LT.N) WRITE(6,390) (IACTV(I),I=1,NACTV)
 280  IF(IIMIN.EQ.2) GOTO 290
      FMIN=FBEST
      CALL DVCOPY(N,X,XMIN)
      GOTO 300
 290  FMAX=-FBEST
      CALL DVCOPY(N,X,XMAX)
 300  CONTINUE
      RETURN
 310  FORMAT('-START OF OPTIMIZATION')
 320  FORMAT(' LOWER BOUNDS', 6(1PD16.6))
 330  FORMAT(' UPPER BOUNDS', 6(1PD16.6))
 340  FORMAT(' MINIMIZATION STEP -- INITIAL FMIN =', 1PD16.6)
 350  FORMAT('0MAXIMIZATION STEP -- INITIAL FMAX =', 1PD16.6)
 360  FORMAT(' X ARRAY'/6(1PD16.6))
 370  FORMAT(1X,I5,' FREE VARIABLES',I5,' FIXED VARIABLES')
 380  FORMAT(' INDICES OF FREE  VARIABLES'/10I8)
 390  FORMAT(' INDICES OF FIXED VARIABLES'/10I8)
 400  FORMAT('0 AFTER ITERATION',I5,' AND',I5,
     1  ' FUNCTION EVALUATIONS, THE FUNCTION VALUE IS',1PD16.6)
 410  FORMAT('0*** FINAL RESULT ***'/' AFTER',I5,
     1    ' ITERATIONS AND', I6,' FUNCTION EVALUATIONS',
     2      ' THE BEST FUNCTION VALUE IS', 1PD17.7)
 420  FORMAT('0 AT ITERATION',I6,' CHECK MULTIPLIERS',
     1    ' FOR THE',I5,' FIXED VARIABLES')
 430  FORMAT(' GRADIENT WITH RESPECT TO FIXED VARIABLES'/
     1             1X,6(1PD16.6))
 440  FORMAT(' EXECUTE LOCAL SEARCH')
 450  FORMAT(1X,I5,' FUNCTION EVALUATIONS AFTER LOCAL SEARCH')
 460  FORMAT(' NORM OF PROJECTED GRADIENT =', 1PD16.6)
      END
Commit	Line	Data
ef94df36	1	*CMZ : 23/08/93 13.30.10 by Jonathan Butterworth
	2	*-- Author :
	3	SUBROUTINE BNDOPT (N,XMIN,XMAX,XLOW,XHI,FMIN,FMAX,FLOBD,FUPBD,X,XT
	4	1EMP,GFREE,PFREE,GACTV,GNEW,AHESS,DELTA,FTOL,GTOL,ETA,ALFMAX,MAXFUN
	5	2,NFCNT,IFREE,IACTV,IPRINT,IRESLT)
	6	INTEGER N, MAXFUN, NFCNT, IPRINT, IRESLT
	7	INTEGER IFREE(N), IACTV(N)
	8	DOUBLE PRECISION FMIN, FMAX, FLOBD, FUPBD, DELTA, FTOL, GTOL,
	9	1 ETA, ALFMAX
	10	DOUBLE PRECISION XMIN(N), XMAX(N), XLOW(N), XHI(N), X(N),
	11	1 XTEMP(N), GFREE(N), PFREE(N), GACTV(N), GNEW(N),
	12	2 AHESS(N,N)
	13	INTEGER I, IBDEL, IBTRUE, IDNEW, II, IIMIN, ILOC, INEW, IPCNT,
	14	1 ITER, ITEST, J, NACTV, NADIM, NFREE
	15	LOGICAL LOCAL, NEGMUL, XALTER
	16	DOUBLE PRECISION A, ALPHA, ALRAT, B, BTOL, B1, D, DEL, DFUN,
	17	1 DVDOT, DXNORM, E, EPSMCH, FA, FBD, FBEST, FDIFF,
	18	2 FOLD, FRAT, FTEST, FTRUE, FU, FV, FW, FY, FZ,
	19	3 GNORM, GTEST1, GTEST2, GTP, GU, OLDF, PE,
	20	4 PNORM, QEPS, R, RR, RTEPS, SCXBD, SFTBND, SS,
	21	5 STEPMX, T, TOL, U, XBEST, XLAMDA, XNORM, XRAT,
	22	6 XV, XW, ZTOL1, ZTOL2
	23	DATA EPSMCH/2.22D-16/
	24	SAVE
	25	RTEPS=SQRT(EPSMCH)
	26	QEPS=SQRT(RTEPS)
	27	ZTOL1=ABS(FTOL)
	28	NADIM=N
	29	NFCNT=0
	30	DO 10 I=1,N
	31	IFREE(I)=0
	32	IACTV(I)=0
	33	10 CONTINUE
	34	IF(IPRINT.LT.0) GOTO 20
	35	WRITE(6,310)
	36	WRITE(6,320) (XLOW(I),I=1,N)
	37	WRITE(6,330) (XHI(I),I=1,N)
	38	20 DO 300 IIMIN=1,2
	39	IF(IIMIN.EQ.2) GOTO 30
	40	CALL DVCOPY(N,XMIN,X)
	41	FTRUE=FMIN
	42	FBEST=FTRUE
	43	FBD=FLOBD
	44	GOTO 40
	45	30 CALL DVCOPY(N,XMAX,X)
	46	FTRUE=FMAX
	47	FBEST=-FTRUE
	48	FBD=FUPBD
	49	40 ITER=0
	50	GNORM=0.0D+0
	51	IPCNT=0
	52	FOLD=FBEST
	53	LOCAL=.FALSE.
	54	DO 60 J=1,N
	55	DO 50 I=1,N
	56	AHESS(I,J)=0.0D+0
	57	50 CONTINUE
	58	AHESS(J,J)=1.0D+0
	59	60 CONTINUE
	60	BTOL=QEPS
	61	70 CALL BNDTST(N,X,XLOW,XHI,BTOL,NFREE,IFREE,NACTV,IACTV,XALTER)
	62	IF(.NOT.XALTER) GOTO 80
	63	FTRUE=DFUN(N,X)
	64	FBEST=FTRUE
65	IF(IIMIN.EQ.2) FBEST=-FTRUE
66	FOLD=FBEST
67	80 IF(IPRINT.LT.0) GOTO 90
68	IF(IIMIN.EQ.1) WRITE(6,340) FTRUE
69	IF(IIMIN.EQ.2) WRITE(6,350) FTRUE
70	IF(LOCAL) WRITE(6,450) NFCNT
71	WRITE(6,360) (X(I),I=1,N)
72	WRITE(6,370) NFREE,NACTV
73	IF(NFREE.GT.0.AND.NFREE.LT.N) WRITE(6,380) (IFREE(I),I=1,NFREE)
74	IF(NACTV.GT.0.AND.NACTV.LT.N) WRITE(6,390) (IACTV(I),I=1,NACTV)
75	90 FTEST=RTEPS*(1.0D+0+ABS(FBD))
76	IF(ABS(FBD-FBEST).LT.FTEST) GOTO 250
77	IF(NFREE.EQ.0) GOTO 250
78	CALL GRDCMP(N,NFREE,IFREE,X,FTRUE,DELTA,XHI,XTEMP,GFREE)
79	NFCNT=NFCNT+NFREE
80	IF(IIMIN.EQ.1) GOTO 110
81	DO 100 I=1,NFREE
82	GFREE(I)=-GFREE(I)
83	100 CONTINUE
84	110 CALL RLEN(NFREE,GFREE,GNORM)
85	IF(GNORM.GT.GTOL.OR.LOCAL) GOTO 120
86	IF(IPRINT.GT.0) WRITE(6,440)
87	DEL=DELTA
88	IF(DELTA.LT.1.0D+0) DEL=SQRT(DELTA)
89	ZTOL2=10.0D+0SQRT(RTEPSDEL)
90	IF(ZTOL2.LT.RTEPS) ZTOL2=RTEPS
91	LOCAL=.TRUE.
92	CALL LOCSCH(IIMIN,N,NFREE,IFREE,X,FBEST,XLOW,XHI,DEL,ZTOL2,NFCNT,
93	1GNEW,FY,XTEMP,FZ,PFREE)
94	FTEST=RTEPS*(1.0D+0+ABS(FBEST))
95	IF(FZ.GE.FBEST.OR.ABS(FZ-FBEST).LT.FTEST) GOTO 250
96	CALL DVCOPY(N,XTEMP,X)
97	FBEST=FZ
98	FTRUE=FZ
99	IF(IIMIN.EQ.2) FTRUE=-FZ
100	GOTO 70
101	120 ITER=ITER+1
102	IF(NFCNT.GT.MAXFUN) GOTO 270
103	IF(IPCNT.GE.IPRINT) IPCNT=0
104	IPCNT=IPCNT+1
105	IF(NFREE.EQ.0) GOTO 250
106	CALL LDLSOL(NFREE,NADIM,AHESS,GFREE,PFREE)
107	DO 130 I=1,NFREE
108	PFREE(I)=-PFREE(I)
109	130 CONTINUE
110	CALL RLEN(NFREE,PFREE,PNORM)
111	PE=PNORM+RTEPS
112	CALL FEASMV(N,NFREE,IFREE,X,PFREE,XLOW,XHI,EPSMCH,STEPMX,INEW,IDN
113	1EW)
114	IF((STEPMX*PE).GT.DELTA) GOTO 140
115	CALL ADDBND(N,NFREE,IFREE,NACTV,IACTV,INEW,IDNEW,NADIM,AHESS,XTEM
116	1P,GFREE,GNORM)
117	ITER=ITER-1
118	GOTO 120
119	140 GTP=DVDOT(NFREE,GFREE,PFREE)
120	XLAMDA=MIN(STEPMX,ALFMAX)
121	U=MIN(1.0D+0,XLAMDA)
122	FU=FBEST
123	GU=GTP
124	ILOC=1
125	SFTBND=DELTA/PE
126	T=RTEPS/PE
127	DO 150 I=1,N
128	XTEMP(I)=X(I)
129	150 CONTINUE
130	160 CALL NEWPTQ(RTEPS,T,ETA,SFTBND,XLAMDA,U,FU,GU,XBEST,FBEST,XW,FW,X
131	1V,FV,A,FA,B,OLDF,B1,SCXBD,E,D,RR,SS,GTEST1,GTEST2,TOL,ILOC,ITEST)
132	IF(ITEST.NE.1) GOTO 180
133	R=XBEST+U
134	DO 170 I=1,NFREE
135	II=IFREE(I)
136	XTEMP(II)=X(II)+R*PFREE(I)
137	170 CONTINUE
138	FU=DFUN(N,XTEMP)
139	NFCNT=NFCNT+1
140	IF(IIMIN.EQ.2) FU=-FU
141	GOTO 160
142	180 IF(ITEST.NE.0) GOTO 250
143	ALPHA=XBEST
144	DO 190 I=1,NFREE
145	II=IFREE(I)
146	X(II)=X(II)+XBEST*PFREE(I)
147	190 CONTINUE
148	FTRUE=FBEST
149	IF(IIMIN.EQ.2) FTRUE=-FBEST
150	IF(IPRINT.LE.0.OR.IPCNT.LT.IPRINT) GOTO 200
151	WRITE(6,400) ITER,NFCNT,FBEST
152	WRITE(6,360) (X(I),I=1,N)
153	WRITE(6,370) NFREE,NACTV
154	IF(NFREE.GT.0.AND.NFREE.LT.N) WRITE(6,380) (IFREE(I),I=1,NFREE)
155	IF(NACTV.GT.0.AND.NACTV.LT.N) WRITE(6,390) (IACTV(I),I=1,NACTV)
156	200 CALL GRDCMP(N,NFREE,IFREE,X,FTRUE,DELTA,XHI,XTEMP,GNEW)
157	CALL RLEN(NFREE,GNEW,GNORM)
158	IF(IPRINT.GT.0.AND.IPCNT.EQ.IPRINT) WRITE(6,460) GNORM
159	IF(IIMIN.EQ.1) GOTO 220
160	DO 210 I=1,NFREE
161	GNEW(I)=-GNEW(I)
162	210 CONTINUE
163	220 NFCNT=NFCNT+NFREE
164	CALL BFGS(NFREE,NADIM,AHESS,EPSMCH,GFREE,GNEW,PFREE,ALPHA,XTEMP)
165	DO 230 I=1,NFREE
166	GFREE(I)=GNEW(I)
167	230 CONTINUE
168	ALRAT=ABS(ALPHA-STEPMX)/STEPMX
169	IF(ALRAT.GE.QEPS) GOTO 240
170	CALL ADDBND(N,NFREE,IFREE,NACTV,IACTV,INEW,IDNEW,NADIM,AHESS,XTEM
171	1P,GFREE,GNORM)
172	GOTO 120
173	240 FDIFF=FOLD-FBEST
174	FRAT=FDIFF/(1.0D+0+ABS(FBEST))
175	IF(FTOL.LT.0.0D+0) FRAT=FDIFF/MAX(ABS(FBEST),EPSMCH)
176	CALL RLEN(N,X,XNORM)
177	DXNORM=ALPHA*PNORM
178	XRAT=DXNORM/(1.0D+0+XNORM)
179	IF(FTOL.LT.0.0D+0) XRAT=DXNORM/MAX(XNORM,EPSMCH)
180	FOLD=FBEST
181	IF(FRAT.GT.ZTOL1.OR.XRAT.GT.ZTOL1) GOTO 120
182	250 IF(NACTV.EQ.0) GOTO 270
183	CALL MULCHK(N,NACTV,IACTV,IIMIN,RTEPS,X,XHI,FTRUE,DELTA,XTEMP,GAC
184	1TV,NEGMUL,IBDEL,IBTRUE)
185	NFCNT=NFCNT+NACTV
186	IF(IPRINT.LE.0.OR.IPCNT.LT.IPRINT) GOTO 260
187	WRITE(6,420) ITER,NACTV
188	WRITE(6,390) (IACTV(I),I=1,NACTV)
189	WRITE(6,430) (GACTV(I),I=1,NACTV)
190	260 IF(.NOT.NEGMUL) GOTO 270
191	CALL DELBND(N,NACTV,IACTV,NFREE,IFREE,IBDEL,IBTRUE,GACTV,NADIM,AH
192	1ESS,GFREE,GNORM)
193	GOTO 120
194	270 IF(IPRINT.LT.0) GOTO 280
195	WRITE(6,410) ITER,NFCNT,FTRUE
196	WRITE(6,360) (X(I),I=1,N)
197	WRITE(6,370) NFREE,NACTV
198	IF(NFREE.GT.0.AND.NFREE.LT.N) WRITE(6,380) (IFREE(I),I=1,NFREE)
199	IF(NACTV.GT.0.AND.NACTV.LT.N) WRITE(6,390) (IACTV(I),I=1,NACTV)
200	280 IF(IIMIN.EQ.2) GOTO 290
201	FMIN=FBEST
202	CALL DVCOPY(N,X,XMIN)
203	GOTO 300
204	290 FMAX=-FBEST
205	CALL DVCOPY(N,X,XMAX)
206	300 CONTINUE
207	RETURN
208	310 FORMAT('-START OF OPTIMIZATION')
209	320 FORMAT(' LOWER BOUNDS', 6(1PD16.6))
210	330 FORMAT(' UPPER BOUNDS', 6(1PD16.6))
211	340 FORMAT(' MINIMIZATION STEP -- INITIAL FMIN =', 1PD16.6)
212	350 FORMAT('0MAXIMIZATION STEP -- INITIAL FMAX =', 1PD16.6)
213	360 FORMAT(' X ARRAY'/6(1PD16.6))
214	370 FORMAT(1X,I5,' FREE VARIABLES',I5,' FIXED VARIABLES')
215	380 FORMAT(' INDICES OF FREE VARIABLES'/10I8)
216	390 FORMAT(' INDICES OF FIXED VARIABLES'/10I8)
217	400 FORMAT('0 AFTER ITERATION',I5,' AND',I5,
218	1 ' FUNCTION EVALUATIONS, THE FUNCTION VALUE IS',1PD16.6)
219	410 FORMAT('0* FINAL RESULT *'/' AFTER',I5,
220	1 ' ITERATIONS AND', I6,' FUNCTION EVALUATIONS',
221	2 ' THE BEST FUNCTION VALUE IS', 1PD17.7)
222	420 FORMAT('0 AT ITERATION',I6,' CHECK MULTIPLIERS',
223	1 ' FOR THE',I5,' FIXED VARIABLES')
224	430 FORMAT(' GRADIENT WITH RESPECT TO FIXED VARIABLES'/
225	1 1X,6(1PD16.6))
226	440 FORMAT(' EXECUTE LOCAL SEARCH')
227	450 FORMAT(1X,I5,' FUNCTION EVALUATIONS AFTER LOCAL SEARCH')
228	460 FORMAT(' NORM OF PROJECTED GRADIENT =', 1PD16.6)
229	END