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tnsunc.f
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************************************************************************
*
*
* Test problems for NonSmooth UNConstrained minimization
*
*
* TNSUNC includes the following subroutines
*
* S STARTX Initiation of variables.
* S FUNC Computation of the value and the subgradient
* of the objective function.
*
*
* Napsu Haarala (2003)
*
* Haarala M., Miettinen K. and Mäkelä M.M.: New Limited Memory
* Bundle Method for Large-Scale Nonsmooth Optimization, Optimization
* Methods and Software, Vol. 19, No. 6, 2004, 673-692.
*
*
************************************************************************
*
* * SUBROUTINE STARTX *
*
*
* * Purpose *
*
*
* Initiation of X.
*
*
* * Calling sequence *
*
* CALL STARTX(N,X,NEXT)
*
*
* * Parameters *
*
* II N Number of variables.
* RO X(N) Vector of variables.
* RI NEXT Problem number.
*
*
* * Problems *
*
* 1. Generalization of MAXQ (convex).
* 2. Generalization of MXHILB (convex).
* 3. Chained LQ (convex).
* 4. Chained CB3 (convex).
* 5. Chained CB3 2 (convex).
* 6. Number of active faces (nonconvex).
* 7. Nonsmooth generalization of Brown function 2 (nonconvex).
* 8. Chained Mifflin 2 (nonconvex).
* 9. Chained crescent (nonconvex).
* 10. Chained crescent 2 (nonconvex).
*
*
* Napsu Haarala (2003)
*
* Haarala M., Miettinen K. and Mäkelä M.M.: New Limited Memory
* Bundle Method for Large-Scale Nonsmooth Optimization, Optimization
* Methods and Software, Vol. 19, No. 6, 2004, 673-692..
*
SUBROUTINE STARTX(N,X,NEXT)
* Scalar Arguments
INTEGER N,NEXT
* Array Arguments
DOUBLE PRECISION X(*)
* Local Arguments
INTEGER I
GOTO(10,20,30,40,40,60,70,80,90,90) NEXT
PRINT*,'Error: Not such a problem.'
NEXT=-1
RETURN
*
* Generalization of MAXQ (convex)
*
10 CONTINUE
DO 11 I=1,N/2
X(I) = DBLE(I)
11 CONTINUE
DO 12 I=N/2+1,N
X(I) = -DBLE(I)
12 CONTINUE
RETURN
*
* Generalization of MXHILB (convex)
*
20 CONTINUE
DO 21 I=1,N
X(I) = 1.0D+00
21 CONTINUE
RETURN
*
* Chained LQ (convex)
*
30 CONTINUE
DO 31 I=1,N
X(I)=-0.50D+00
31 CONTINUE
RETURN
*
* Chained CB3 1 and 2 (convex)
*
40 CONTINUE
DO 41 I=1,N
X(I)=2.0D+00
41 CONTINUE
RETURN
*
* Number of active faces (nonconvex)
*
60 CONTINUE
DO 61 I=1,N
X(I) = 1.0D+00
61 CONTINUE
RETURN
*
* Nonsmooth generalization of Brown function 2 (nonconvex)
*
70 CONTINUE
DO 71 I=1,N
IF(MOD(I,2) .EQ. 1) THEN
X(I) = -1.0D+00
ELSE
X(I) = 1.0D+00
ENDIF
71 CONTINUE
RETURN
*
* Chained Mifflin 2 (nonconvex)
*
80 CONTINUE
DO 81 I=1,N
X(I) = -1.0D+00
81 CONTINUE
RETURN
*
* Chained crescent (nonconvex)
*
90 CONTINUE
DO 91 I=1,N
IF(MOD(I,2) .EQ. 1) THEN
X(I) = -1.50D+00
ELSE
X(I) = 2.0D+00
ENDIF
91 CONTINUE
RETURN
END
************************************************************************
*
* * SUBROUTINE FUNC *
*
*
* * Purpose *
*
*
* Computation of the value and the subgradient of the objective
* function.
*
*
* * Calling sequence *
*
* CALL FUNC(N,X,F,G,NEXT)
*
*
* * Parameters *
*
* II N Number of variables.
* RI X(N) Vector of variables.
* RI NEXT Problem number.
* RO F Value of the objective function.
* RO G(N) Subgradient of the objective function.
*
*
* * Problems *
*
* 1. Generalization of MAXQ (convex).
* 2. Generalization of MXHILB (convex).
* 3. Chained LQ (convex).
* 4. Chained CB3 (convex).
* 5. Chained CB3 2 (convex).
* 6. Number of active faces (nonconvex).
* 7. Nonsmooth generalization of Brown function 2 (nonconvex).
* 8. Chained Mifflin 2 (nonconvex).
* 9. Chained crescent (nonconvex).
* 10. Chained crescent 2 (nonconvex).
*
*
* Napsu Haarala (2003)
*
* Haarala M., Miettinen K. and Mäkelä M.M.: New Limited Memory
* Bundle Method for Large-Scale Nonsmooth Optimization, Optimization
* Methods and Software, Vol. 19, No. 6, 2004, 673-692..
*
*
SUBROUTINE FUNC(N,X,F,G,NEXT)
* Scalar Arguments
INTEGER N,NEXT
DOUBLE PRECISION F
* Array Arguments
DOUBLE PRECISION G(*),X(*)
* Local Arguments
INTEGER I,J,HIT
DOUBLE PRECISION Y,TEMP2,TEMP3,A,B,C,D,P,Q
* Intrinsic Functions
INTRINSIC DABS,DMAX1,SIGN,DLOG,DEXP,DCOS,DSIN
GOTO(10,20,30,40,50,60,70,80,90,100) NEXT
PRINT*,'Error: Not such a problem.'
NEXT=-1
RETURN
*
* Generalization of MAXQ (convex)
*
10 CONTINUE
F=X(1)*X(1)
G(1)=0.0D+00
HIT=1
DO 11 I=2,N
Y=X(I)*X(I)
IF (Y .GT. F) THEN
F=Y
HIT=I
END IF
G(I)=0.0D+00
11 CONTINUE
G(HIT)=2*X(HIT)
RETURN
*
* Generalization of MXHILB (convex)
*
20 CONTINUE
F = 0.0D+00
HIT=1
DO 21 J = 1,N
F = F + X(J)/DBLE(J)
21 CONTINUE
G(1)=SIGN(1.0D+00,F)
F = DABS(F)
DO 22 I = 2,N
TEMP2 = 0.0D0
DO 23 J = 1,N
TEMP2 = TEMP2 + X(J)/DBLE(I+J-1)
23 CONTINUE
G(I)=SIGN(1.0D+00,TEMP2)
TEMP2 = DABS(TEMP2)
IF (TEMP2 .GT. F) THEN
F=TEMP2
HIT=I
END IF
22 CONTINUE
TEMP3=G(HIT)
DO 24 J = 1,N
G(J) = TEMP3/DBLE(HIT+J-1)
24 CONTINUE
RETURN
*
* Chained LQ (convex)
*
30 CONTINUE
F=0.0D+00
G(1)=0.0D+00
DO 31 I=1,N-1
G(I+1)=0.0D+00
A = -X(I)-X(I+1)
B = -X(I)-X(I+1)+(X(I)*X(I)+X(I+1)*X(I+1)-1.0D+00)
IF (A .GE. B) THEN
F=F+A
G(I)=G(I)-1.0D+00
G(I+1)=-1.0D+00
ELSE
F=F+B
G(I)=G(I)-1.0D+00+2.0D+00*X(I)
G(I+1)=-1.0D+00+2.0D+00*X(I+1)
ENDIF
31 CONTINUE
RETURN
*
* Chained CB3 (convex)
*
40 CONTINUE
F=0.0D+00
G(1)=0.0D+00
DO 41 I=1,N-1
G(I+1)=0.0D+00
A=X(I)*X(I)*X(I)*X(I)+X(I+1)*X(I+1)
B=(2.0D+00-X(I))*(2.0D+00-X(I))+
& (2.0D+00-X(I+1))*(2.0D+00-X(I+1))
C= 2.0D+00*DEXP(-X(I)+X(I+1))
Y=DMAX1(A,B)
Y=DMAX1(Y,C)
IF (Y .EQ. A) THEN
G(I)=G(I)+4.0D+00*X(I)*X(I)*X(I)
G(I+1)=2.0D+00*X(I+1)
ELSE IF (Y .EQ. B) THEN
G(I)=G(I)+2.0D+00*X(I)-4.0D+00
G(I+1)=2.0D+00*X(I+1)-4.0D+00
ELSE
G(I)= G(I) - C
G(I+1)= C
END IF
F=F+Y
41 CONTINUE
RETURN
*
* Chained CB3 2 (convex)
*
50 CONTINUE
F=0.0D+00
G(1)=0.0D+00
A=0.0D+00
B=0.0D+00
C=0.0D+00
DO 51 I=1,N-1
G(I+1)=0.0D+00
A=A+X(I)*X(I)*X(I)*X(I)+X(I+1)*X(I+1)
B=B+(2.0D+00-X(I))*(2.0D+00-X(I))+
& (2.0D+00-X(I+1))*(2.0D+00-X(I+1))
C=C+2.0D+00*DEXP(-X(I)+X(I+1))
51 CONTINUE
F=DMAX1(A,B)
F=DMAX1(F,C)
IF (F .EQ. A) THEN
DO 53 I=1,N-1
G(I)=G(I)+4.0D+00*X(I)*X(I)*X(I)
G(I+1)=2.0D+00*X(I+1)
53 CONTINUE
ELSE IF (F .EQ. B) THEN
DO 54 I=1,N-1
G(I)=G(I)+2.0D+00*X(I)-4.0D+00
G(I+1)=2.0D+00*X(I+1)-4.0D+00
54 CONTINUE
ELSE
DO 55 I=1,N-1
G(I)= G(I) - 2.0D+00*DEXP(-X(I)+X(I+1))
G(I+1)= 2.0D+00*DEXP(-X(I)+X(I+1))
55 CONTINUE
END IF
RETURN
*
* Number of active faces (nonconvex)
*
60 CONTINUE
TEMP3=1.0D+00
Y=-X(1)
G(1)= 0.0D+00
F=DLOG(DABS(X(1))+1.0D+00)
HIT=1
TEMP2=F
DO 62 I=2,N
Y=Y - X(I)
G(I)= 0.0D+00
F=DMAX1(F,DLOG(DABS(X(I))+1.0D+00))
IF(F .GT. TEMP2) THEN
HIT=I
TEMP2=F
END IF
62 CONTINUE
F=DMAX1(F,DLOG(DABS(Y)+1.0D+00))
IF(F .GT. TEMP2) THEN
IF (Y.GE.0.0D+00) TEMP3=-1.0D+00
DO 63 I=1,N
G(I)= TEMP3*(1.0D+00/(DABS(Y)+1.0D+00))
63 CONTINUE
ELSE
IF (X(HIT).LT.0.0D+00) TEMP3=-1.0D+00
G(HIT)=TEMP3*(1.0D+00/(DABS(X(HIT))+1.0D+00))
END IF
RETURN
*
* Nonsmooth generalization of Brown function 2 (nonconvex)
*
70 CONTINUE
F=0.0D+00
G(1)=0.0D+00
DO 71 I=1,N-1
A=DABS(X(I))
B=DABS(X(I+1))
C=X(I)*X(I)+1.0D+00
D=X(I+1)*X(I+1)+1.0D+00
F=F+B**C+A**D
P=0.0D+00
Q=0.0D+00
IF (X(I).LT.0.0D+00) THEN
IF (B .GT. P) P=DLOG(B)
G(I)=G(I)-D*A**(D-1.0D+00)+2.0D+00*X(I)*P*B**C
ELSE
IF (B .GT. P) P=DLOG(B)
G(I)=G(I)+D*A**(D-1.0D+00)+2.0D+00*X(I)*P*B**C
ENDIF
IF (X(I+1).EQ.0.0D+00) THEN
G(I+1)=0.0D+00
ELSE IF (X(I+1).LT.0.0D+00) THEN
IF (A .GT. Q) Q=DLOG(A)
G(I+1)=-C*B**(C-1.0D+00)+2.0D+00*X(I+1)*Q*A**D
ELSE
IF (A .GT. Q) Q=DLOG(A)
G(I+1)=C*B**(C-1.0D+00)+2.0D+00*X(I+1)*Q*A**D
ENDIF
71 CONTINUE
RETURN
*
* Chained mifflin 2 (nonconvex)
*
80 CONTINUE
F=0.0D+00
G(1)=0.0D+00
DO 81 I=1,N-1
Y = X(I)*X(I) + X(I+1)*X(I+1) - 1.0D0
F = F -X(I) + 2.0D+00*Y + 1.75D+00*DABS(Y)
Y = SIGN(3.5D+00,Y) + 4.0D+00
G(I) = G(I) + Y*X(I) - 1.0D+00
G(I+1) = Y*X(I+1)
81 CONTINUE
RETURN
*
* Chained crescent (nonconvex)
*
90 CONTINUE
TEMP2=0.0D+00
TEMP3=0.0D+00
DO 91 I=1,N-1
TEMP2 = TEMP2 + X(I)*X(I) + (X(I+1)-1.0D+00)*(X(I+1)-1.0D+00)
& + X(I+1) - 1.0D+00
TEMP3 = TEMP3 - X(I)*X(I) - (X(I+1)-1.0D+00)*(X(I+1)-1.0D+00)
& + X(I+1) + 1.0D+00
91 CONTINUE
F = DMAX1(TEMP2,TEMP3)
G(1)=0.0D+00
IF (TEMP2 .GE. TEMP3) THEN
DO 92 I=1,N-1
G(I)=G(I)+2.0D+00*X(I)
G(I+1)=2.0D+00*(X(I+1)-1.0D+00) + 1.0D+00
92 CONTINUE
ELSE
DO 93 I=1,N-1
G(I)=G(I)-2.0D+00*X(I)
G(I+1)=-2.0D+00*(X(I+1)-1.0D+00) + 1.0D+00
93 CONTINUE
END IF
RETURN
*
* Chained crescent 2 (nonconvex)
*
100 CONTINUE
F=0.0D+00
G(1)=0.0D+00
DO 101 I=1,N-1
TEMP2 = X(I)*X(I) + (X(I+1)-1.0D+00)*(X(I+1)-1.0D+00)
& + X(I+1) - 1.0D+00
TEMP3 = - X(I)*X(I) - (X(I+1)-1.0D+00)*(X(I+1)-1.0D+00)
& + X(I+1) + 1.0D+00
IF (TEMP2 .GE. TEMP3) THEN
F=F+TEMP2
G(I)=G(I)+2.0D+00*X(I)
G(I+1)=2.0D+00*(X(I+1)-1.0D+00) + 1.0D+00
ELSE
F=F+TEMP3
G(I)=G(I)-2.0D+00*X(I)
G(I+1)=-2.0D+00*(X(I+1)-1.0D+00) + 1.0D+00
END IF
101 CONTINUE
RETURN
END