*------------------------------------------------------------
* March 8, 2000
* Propane, Isobutane, n-Butane Isopentane Separation    
*
* Floudas & Pardalos, 
* A collection of test problems for constrained global
* optimization algorithms.
* Springer-Verlag, Berlin, 1990.
* Lecture Notes in Computer Science, vol.455.
* Problem 5.3, pp.41-46.
*
* Dr. Neculai Andrei
* Research Institute for Informatics,
* 8-10, Averescu Avenue, Bucharest 1, Romania
* E-mail: nandrei@u3.ici.ro
* web: www.ici.ro/camo
*------------------------------------------------------------
*
	subroutine ini(n,m,mb,me,sb,x,icgc,ipgc,icge,ipge,
     1                 nszc,nsze,nb)
*

	double precision x(n)
	integer sb(mb)
	integer icgc(nszc),ipgc(n+1)
	integer icge(nsze),ipge(n+1)

*
* Information about the problem.
*
	write(1,10)
10	format(5x,'Example of nonlinear programming.')
	write(1,11)
11	format(5x,'Propane, Isobutane, n-Butane Isopentane separation')
	write(1,14)
14	format(5x,'Floudas & Pardalos, Problem 5.3, pp.41-46.')
	write(1,15)
15	format(5x,'March 11, 2001')
*
* Dimension of the problem:
*
	n=110          ! No. of variables.
	m=0           ! No. of inequality constraints.
	me=68         ! No. of equality constraints.
	mb=12        ! No. of simple bounds on variables.
	nszc=0        ! No. of non-zeros in Jacobian of c(x)>=0.
	nsze=n*me     ! No. of non-zeros in Jacobian of e(x) =0.

*
* Initial point:
*          
      do i=1,n
        x(i)=1.d0
      end do  
*
	do i=33,38
	  x(i)=0.9d0
	end do
*
* Index vector for simple bounds: cb >= 0.
*          
      j=1
      do i=33,38
	  sb(j)=i
	  sb(j+1)=-i
	  j=j+2
      end do
*
* Rows indices of the nonzeros of the Jacobian of the Equalities
*
*
* Starting address of columns of the Jacobian of the Equalities
*
*
* Rows indices of the nonzeros of the Jacobian of the INEqualities
*                
      k=1
      do i=1,n
        do j=1,me
          icge(k)=j
          k=k+1
        end do
      end do    
*
* Starting address of columns of the Jacobian of the INEqualities
*
      ipge(1)=1
      do i=2,n+1
        ipge(i)=me*(i-1)+1
      end do  
*
	return
	end
	
	
*--------------------------------------------------------------
* March 8, 2000
* Propane, Isobutane, n-Butane Isopentane Separation
* Floudas & Pardalos, Problem 5.3, pp.41-46.
*--------------------------------------------------------------
*
	subroutine prob(n,m,mb,me,sb,x,objf,gobj,c,gc,cb,e,ge,
     1                  nszc,nsze,nb)
*
* Calculate problem function at iterate x.
*
	double precision x(n),objf,gobj(n),c(m),gc(nszc)
	double precision cb(mb),e(me),ge(nsze)
*	
	real*8 a01,a11,a21,a31,ba1,bb1,bc1
	real*8 a02,a12,a22,a32,ba2,bb2,bc2
	real*8 a03,a13,a23,a33,ba3,bb3,bc3
*
      real*8 gjac(68,110)
*
	a01=0.31569d0
	a11=-0.0112812d0
	a21=0.0072698d0
	a31=0.0064241d0
	ba1=0.0016446d0
	bb1=0.0018611d0
	bc1=0.001262d0
*
	a02=0.96926d0
	a12=-0.0413393d0
	a22=0.0228203d0
	a32=0.0257035d0
	ba2=0.0015625d0
	bb2=0.0091604d0
	bc2=0.0076758d0
*	
	a03=0.40281d0
	a13=-0.0119785d0
	a23=0.0082055d0
	a33=0.009819d0
	ba3=-0.001748d0
	bb3=-0.0002583d0
	bc3=-0.0004691d0
*
* Objective function and its gradient:
*
	objf=a01 + (a11+a21*x(33)+a31*x(36)+ba1*x(39)+
     *                            bb1*x(40)+bc1*x(41) ) * x(6) +
     *     a02 + (a12+a22*x(34)+a32*x(37)+ba2*x(59)+
     *                            bb2*x(60)+bc2*x(61) ) * x(15) +    
     *     a03 + (a13+a23*x(35)+a33*x(38)+ba3*x(79)+
     *                            bb3*x(80)+bc3*x(81) ) * x(24)
*
	do i=1,n
	  gobj(i)=0.d0
	end do                
*	         
      gobj(6)=a11+a21*x(33)+a31*x(36)+ba1*x(39)+bb1*x(40)+bc1*x(41)
	gobj(33)=a21*x(6)
	gobj(36)=a31*x(6)          
	gobj(39)=ba1*x(6)
	gobj(40)=bb1*x(6)
	gobj(41)=bc1*x(6)
*
      gobj(15)=a12+a22*x(34)+a32*x(37)+ba2*x(59)+bb2*x(60)+bc2*x(61)
	gobj(34)=a22*x(15)
	gobj(37)=a32*x(15)
	gobj(59)=ba2*x(15)
	gobj(60)=bb2*x(15)
	gobj(61)=bc2*x(15)
*
      gobj(24)=a13+a23*x(35)+a33*x(38)+ba3*x(79)+bb3*x(80)+bc3*x(81)
      gobj(35)=a23*x(24)
      gobj(38)=a33*x(24)
      gobj(79)=ba3*x(24)
      gobj(80)=bb3*x(24)
      gobj(81)=bc3*x(24)
*
* Bounds on variables:
*        
*      j=1
*	do i=1,32
*	  cb(j)=x(i)  
*	  cb(j+1)=200.d0-x(i)
*	  j=j+2
*	end do 
    
      cb(1)=x(33)-0.85d0
      cb(2)=1.d0-x(33)
      cb(3)=x(34)-0.85d0
      cb(4)=1.d0-x(34)
      cb(5)=x(35)-0.85d0
      cb(6)=1.d0-x(35)
      cb(7)=x(36)-0.85d0
      cb(8)=1.d0-x(36)
      cb(9)=x(37)-0.85d0
      cb(10)=1.d0-x(37)
      cb(11)=x(38)-0.85d0
      cb(12)=1.d0-x(38)
*      
*      j=77
*	do i=39,n
*	  cb(j)=x(i)  
*	  cb(j+1)=200.d0-x(i)
*	  j=j+2
*	end do 
*
* Constraints. (Equalities):
*
      e(1)=x(1)+x(2)+x(3)+x(4)+x(5)-600.d0
      e(2)=x(7)-x(8)-x(9)
      e(3)=x(10)-x(11)-x(12)-x(13)-x(14)
      e(4)=x(16)-x(17)-x(18)-x(19)
      e(5)=x(20)-x(21)-x(22)-x(23)
      e(6)=x(25)-x(26)-x(27)-x(28)-x(29)
      e(7)=x(30)-x(31)-x(32)
*      
      e(8)=x(7)*x(43)-x(33)*x(91)
      e(9)=x(16)*x(64)-x(34)*x(96)
      e(10)=x(25)*x(85)-x(35)*x(101)
      e(11)=x(10)*x(48)-x(36)*x(92)
      e(12)=x(20)*x(73)-x(37)*x(97)
      e(13)=x(30)*x(90)-x(38)*x(102)
*      
      e(14)=x(91)-x(6)*x(39)
      e(15)=x(92)-x(6)*x(40)
      e(16)=x(93)-x(6)*x(41)
      e(17)=x(94)-x(6)*x(42)
*      
      e(18)=x(95)-x(15)*x(59)
      e(19)=x(96)-x(15)*x(60)
      e(20)=x(97)-x(15)*x(61)
      e(21)=x(98)-x(15)*x(62)
*      
      e(22)=x(99) -x(24)*x(79)
      e(23)=x(100)-x(24)*x(80)
      e(24)=x(101)-x(24)*x(81)
      e(25)=x(102)-x(24)*x(82)
*      
      e(26)=x(91)-x(7)*x(43)-x(10)*x(47)
      e(27)=x(92)-x(7)*x(44)-x(10)*x(48)
      e(28)=x(93)-x(7)*x(45)-x(10)*x(49)
      e(29)=x(94)-x(7)*x(46)-x(10)*x(50)
*      
      e(30)=x(95)-x(16)*x(63)-x(20)*x(71)
      e(31)=x(96)-x(16)*x(64)-x(20)*x(72)
      e(32)=x(97)-x(16)*x(65)-x(20)*x(73)
      e(33)=x(98)-x(16)*x(66)-x(20)*x(74)
*      
      e(34)=x(99) -x(25)*x(83)-x(30)*x(87)
      e(35)=x(100)-x(25)*x(84)-x(30)*x(88)
      e(36)=x(101)-x(25)*x(85)-x(30)*x(89)
      e(37)=x(102)-x(25)*x(86)-x(30)*x(90)
*      
      e(38)=0.250d0*x(1)+x(17)*x(67)+x(26)*x(103)-x(91)
      e(39)=0.333d0*x(1)+x(17)*x(68)+x(26)*x(104)-x(92)
      e(40)=0.167d0*x(1)+x(17)*x(69)+x(26)*x(105)-x(93)
      e(41)=0.250d0*x(1)+x(17)*x(70)+x(26)*x(106)-x(91)
*      
      e(42)=0.250d0*x(2)+x(11)*x(51)+x(27)*x(107)-x(95)
      e(43)=0.333d0*x(2)+x(11)*x(52)+x(27)*x(108)-x(96)
      e(44)=0.167d0*x(2)+x(11)*x(53)+x(27)*x(109)-x(97)
      e(45)=0.250d0*x(2)+x(11)*x(54)+x(27)*x(110)-x(95)
*      
      e(46)=0.250d0*x(3)+x(12)*x(55)+x(21)*x(75)-x(99)
      e(47)=0.333d0*x(3)+x(12)*x(56)+x(21)*x(76)-x(100)
      e(48)=0.167d0*x(3)+x(12)*x(57)+x(21)*x(77)-x(101)
      e(49)=0.250d0*x(3)+x(12)*x(58)+x(21)*x(78)-x(99)
*      
      e(50)=x(45)
      e(51)=x(46)
      e(52)=x(66)
      e(53)=x(71)
      e(54)=x(87)
      e(55)=x(88)
*      
      e(56)=0.250d0*x(4)+x(8)*x(43)+x(13)*x(47)+x(18)*x(63)+
     *                     x(22)*x(71)+x(28)*x(83)+x(31)*x(87)-50.d0
      e(57)=0.222d0*x(4)+x(8)*x(44)+x(13)*x(48)+x(18)*x(64)+
     *                     x(22)*x(72)+x(28)*x(84)+x(31)*x(88)-100.d0
      e(58)=0.167d0*x(4)+x(8)*x(45)+x(13)*x(49)+x(18)*x(65)+
     *                     x(22)*x(73)+x(28)*x(85)+x(31)*x(89)-40.d0
      e(59)=0.250d0*x(4)+x(8)*x(46)+x(13)*x(50)+x(18)*x(66)+
     *                     x(22)*x(74)+x(28)*x(86)+x(31)*x(90)-100.d0
*      
      e(60)=x(39)+x(40)+x(41)+x(42)-1.d0
      e(61)=x(43)+x(44)+x(45)+x(46)-1.d0
      e(62)=x(47)+x(48)+x(49)+x(50)-1.d0
      e(63)=x(59)+x(60)+x(61)+x(62)-1.d0
      e(64)=x(63)+x(64)+x(65)+x(66)-1.d0
      e(65)=x(71)+x(72)+x(73)+x(74)-1.d0
      e(66)=x(79)+x(80)+x(81)+x(82)-1.d0
      e(67)=x(83)+x(84)+x(85)+x(86)-1.d0
      e(68)=x(87)+x(88)+x(89)+x(90)-1.d0
*
*
* Jacobian of inequalities constraints
*               
      do i=1,me
        do j=1,n
          gjac(i,j)=0.d0
        end do
      end do
*                
*e1
      gjac(1,1)=1.d0
      gjac(1,2)=1.d0
      gjac(1,3)=1.d0
      gjac(1,4)=1.d0
      gjac(1,5)=1.d0
*e2      
      gjac(2,7)=1.d0
      gjac(2,8)=-1.d0
      gjac(2,9)=-1.d0
*e3      
      gjac(3,10)=1.d0
      gjac(3,11)=-1.d0
      gjac(3,12)=-1.d0
      gjac(3,13)=-1.d0
      gjac(3,14)=-1.d0
*e4      
      gjac(4,16)=1.d0
      gjac(4,17)=-1.d0 
      gjac(4,18)=-1.d0
      gjac(4,19)=-1.d0
*e5      
      gjac(5,20)=1.d0
      gjac(5,21)=-1.d0
      gjac(5,22)=-1.d0
      gjac(5,23)=-1.d0
*e6      
      gjac(6,25)=1.d0
      gjac(6,26)=-1.d0
      gjac(6,27)=-1.d0
      gjac(6,28)=-1.d0
      gjac(6,29)=-1.d0
*e7      
      gjac(7,30)=1.d0
      gjac(7,31)=-1.d0
      gjac(7,32)=-1.d0
*e8      
      gjac(8,7)=x(43)
      gjac(8,43)=x(7)
      gjac(8,33)=-x(91)
      gjac(8,91)=-x(33)
*e9      
      gjac(9,16)=x(64)
      gjac(9,64)=x(16)
      gjac(9,34)=-x(96)
      gjac(9,96)=-x(34)
*e10      
      gjac(10,25)=x(85)
      gjac(10,85)=x(25)
      gjac(10,35)=-x(101)
      gjac(10,101)=-x(35)
*e11      
      gjac(11,10)=x(48)
      gjac(11,48)=x(10)
      gjac(11,36)=-x(92)
      gjac(11,92)=-x(36) 
*e12      
      gjac(12,20)=x(73)
      gjac(12,73)=x(20)
      gjac(12,37)=-x(97)
      gjac(12,97)=-x(37)
*e13      
      gjac(13,30)=x(90)
      gjac(13,90)=x(30)
      gjac(13,38)=-x(102)
      gjac(13,102)=-x(38) 
*e14      
      gjac(14,91)=1.d0
      gjac(14,6)=-x(39)
      gjac(14,39)=-x(6)
*e15      
      gjac(15,92)=1.d0
      gjac(15,6)=-x(40)
      gjac(15,40)=-x(6)
*e16      
      gjac(16,93)=1.d0
      gjac(16,6)=-x(41)
      gjac(16,41)=-x(6)
*e17      
      gjac(17,94)=1.d0
      gjac(17,6)=-x(42)
      gjac(17,42)=-x(6)
*e18      
      gjac(18,95)=1.d0
      gjac(18,15)=-x(59)
      gjac(18,59)=-x(15)
*e19      
      gjac(19,96)=1.d0
      gjac(19,15)=-x(60)
      gjac(19,60)=-x(15)
*e20      
      gjac(20,97)=1.d0
      gjac(20,15)=-x(61)
      gjac(20,61)=-x(15)
*e21      
      gjac(21,98)=1.d0
      gjac(21,15)=-x(62)
      gjac(21,62)=-x(15) 
*e22      
      gjac(22,99)=1.d0
      gjac(22,24)=-x(79)
      gjac(22,79)=-x(24)
*e23      
      gjac(23,100)=1.d0
      gjac(23,24)=-x(80)
      gjac(23,80)=-x(24) 
*e24      
      gjac(24,101)=1.d0
      gjac(24,24)=-x(81)
      gjac(24,81)=-x(24)
*e25      
      gjac(25,102)=1.d0
      gjac(25,24)=-x(82)
      gjac(25,82)=-x(24)
*e26      
      gjac(26,91)=1.d0
      gjac(26,7)=-x(43)
      gjac(26,43)=-x(7)
      gjac(26,10)=-x(47)
      gjac(26,47)=-x(10)
*e27      
      gjac(27,92)=1.d0
      gjac(27,7)=-x(44)
      gjac(27,44)=-x(7)
      gjac(27,10)=-x(48)
      gjac(27,48)=-x(10)
*e28      
      gjac(28,93)=1.d0
      gjac(28,7)=-x(45)
      gjac(28,45)=-x(7)
      gjac(28,10)=-x(49)
      gjac(28,49)=-x(10)
*e29      
      gjac(29,94)=1.d0
      gjac(29,7)=-x(46)
      gjac(29,46)=-x(7)
      gjac(29,10)=-x(50)
      gjac(29,50)=-x(10) 
*e30      
      gjac(30,95)=1.d0
      gjac(30,16)=-x(63)
      gjac(30,63)=-x(16)
      gjac(30,20)=-x(71)
      gjac(30,71)=-x(20) 
*e31      
      gjac(31,96)=1.d0
      gjac(31,16)=-x(64)
      gjac(31,64)=-x(16)
      gjac(31,20)=-x(72)
      gjac(31,72)=-x(20)
*e32      
      gjac(32,97)=1.d0
      gjac(32,16)=-x(65)
      gjac(32,65)=-x(16)
      gjac(32,20)=-x(73)
      gjac(32,73)=-x(20)
*e33      
      gjac(33,98)=1.d0
      gjac(33,16)=-x(66)
      gjac(33,66)=-x(16)
      gjac(33,20)=-x(74)
      gjac(33,74)=-x(20)
*e34      
      gjac(34,99)=1.d0
      gjac(34,25)=-x(83)
      gjac(34,83)=-x(25)
      gjac(34,30)=-x(87)
      gjac(34,87)=-x(30)
*e35      
      gjac(35,100)=1.d0
      gjac(35,25)=-x(84)
      gjac(35,84)=-x(25)
      gjac(35,30)=-x(88)
      gjac(35,88)=-x(30) 
*e36      
      gjac(36,101)=1.d0
      gjac(36,25)=-x(85)
      gjac(36,85)=-x(25)
      gjac(36,30)=-x(89)
      gjac(36,89)=-x(30)  
*e37      
      gjac(37,102)=1.d0
      gjac(37,25)=-x(86)
      gjac(37,86)=-x(25)
      gjac(37,30)=-x(90)
      gjac(37,90)=-x(30) 
*e38      
      gjac(38,1)=0.250d0
      gjac(38,17)=x(67)
      gjac(38,67)=x(17) 
      gjac(38,26)=x(103)
      gjac(38,103)=x(26)
      gjac(38,91)=-1.d0
*e39      
      gjac(39,1)=0.333d0
      gjac(39,17)=x(68)
      gjac(39,68)=x(17)
      gjac(39,26)=x(104)
      gjac(39,104)=x(26)
      gjac(39,92)=-1.d0
*e40      
      gjac(40,1)=0.167d0
      gjac(40,17)=x(69)
      gjac(40,69)=x(17)
      gjac(40,26)=x(105)
      gjac(40,105)=x(26)
      gjac(40,93)=-1.d0
*e41      
      gjac(41,1)=0.250d0
      gjac(41,17)=x(70)
      gjac(41,70)=x(17)
      gjac(41,26)=x(106)
      gjac(41,106)=x(26)
      gjac(41,91)=-1.d0
*e42      
      gjac(42,2)=0.250d0
      gjac(42,11)=x(51)
      gjac(42,51)=x(11)
      gjac(42,27)=x(107)
      gjac(42,107)=x(27)
      gjac(42,95)=-1.d0
*e43      
      gjac(43,2)=0.333d0
      gjac(43,11)=x(52)
      gjac(43,52)=x(11)
      gjac(43,27)=x(108)
      gjac(43,108)=x(27)
      gjac(43,96)=-1.d0
*e44      
      gjac(44,2)=0.167d0
      gjac(44,11)=x(53)
      gjac(44,53)=x(11)
      gjac(44,27)=x(109)
      gjac(44,109)=x(27)
      gjac(44,97)=-1.d0
*e45      
      gjac(45,2)=0.250d0
      gjac(45,11)=x(54)
      gjac(45,54)=x(11)
      gjac(45,27)=x(110)
      gjac(45,110)=x(27)
      gjac(45,95)=-1.d0
*e46      
      gjac(46,3)=0.250d0
      gjac(46,12)=x(55)
      gjac(46,55)=x(12)      
      gjac(46,21)=x(75)
      gjac(46,75)=x(21)
      gjac(46,99)=-1.d0
*e47      
      gjac(47,3)=0.333d0
      gjac(47,12)=x(56)
      gjac(47,56)=x(12)
      gjac(47,21)=x(76)
      gjac(47,76)=x(21)
      gjac(47,100)=-1.d0
*e48      
      gjac(48,3)=0.167d0
      gjac(48,12)=x(57)
      gjac(48,57)=x(12)
      gjac(48,21)=x(77)
      gjac(48,77)=x(21)
      gjac(48,101)=-1.d0   
*e49      
      gjac(49,3)=0.250d0
      gjac(49,12)=x(58)
      gjac(49,58)=x(12)
      gjac(49,21)=x(78)
      gjac(49,78)=x(21)
      gjac(49,99)=-1.d0
*e50-55      
      gjac(50,45)=1.d0
      gjac(51,46)=1.d0
      gjac(52,66)=1.d0
      gjac(53,71)=1.d0
      gjac(54,87)=1.d0
      gjac(55,88)=1.d0
*e56      
      gjac(56,4)=0.250d0
      gjac(56,8)=x(43)
      gjac(56,43)=x(8)
      gjac(56,13)=x(47)
      gjac(56,47)=x(13)
      gjac(56,18)=x(63)
      gjac(56,63)=x(18)
      gjac(56,22)=x(71)
      gjac(56,71)=x(22)
      gjac(56,28)=x(83)
      gjac(56,83)=x(28)
      gjac(56,31)=x(87)
      gjac(56,87)=x(31)
*e57      
      gjac(57,4)=0.222d0
      gjac(57,8)=x(44)
      gjac(57,44)=x(8)
      gjac(57,13)=x(48)
      gjac(57,48)=x(13)
      gjac(57,18)=x(64)
      gjac(57,64)=x(18)
      gjac(57,22)=x(72)
      gjac(57,72)=x(22)
      gjac(57,28)=x(84)
      gjac(57,84)=x(28)
      gjac(57,31)=x(88)
      gjac(57,88)=x(31)
*e58      
      gjac(58,4)=0.167d0
      gjac(58,8)=x(45)
      gjac(58,45)=x(8)
      gjac(58,13)=x(49)
      gjac(58,49)=x(13)
      gjac(58,18)=x(65)
      gjac(58,65)=x(18)
      gjac(58,22)=x(73)
      gjac(58,73)=x(22)
      gjac(58,28)=x(85)
      gjac(58,85)=x(28)
      gjac(58,31)=x(89)
      gjac(58,89)=x(31)
*e59      
      gjac(59,4)=0.250d0
      gjac(59,8)=x(46)
      gjac(59,46)=x(8)
      gjac(59,13)=x(50)
      gjac(59,50)=x(13)
      gjac(59,18)=x(66)
      gjac(59,66)=x(18)
      gjac(59,22)=x(74)
      gjac(59,74)=x(22)
      gjac(59,28)=x(86)
      gjac(59,86)=x(28)
      gjac(59,31)=x(90)
      gjac(59,90)=x(31)
*e60      
      gjac(60,39)=1.d0
      gjac(60,40)=1.d0
      gjac(60,41)=1.d0
      gjac(60,42)=1.d0
      
      gjac(61,43)=1.d0
      gjac(61,44)=1.d0
      gjac(61,45)=1.d0
      gjac(61,46)=1.d0
      
      gjac(62,47)=1.d0
      gjac(62,48)=1.d0
      gjac(62,49)=1.d0
      gjac(62,50)=1.d0
      
      gjac(63,59)=1.d0
      gjac(63,60)=1.d0
      gjac(63,61)=1.d0
      gjac(63,62)=1.d0
      
      gjac(64,63)=1.d0
      gjac(64,64)=1.d0
      gjac(64,65)=1.d0
      gjac(64,66)=1.d0
      
      gjac(65,71)=1.d0
      gjac(65,72)=1.d0
      gjac(65,73)=1.d0
      gjac(65,74)=1.d0
      
      gjac(66,79)=1.d0
      gjac(66,80)=1.d0
      gjac(66,81)=1.d0
      gjac(66,82)=1.d0
      
      gjac(67,83)=1.d0
      gjac(67,84)=1.d0
      gjac(67,85)=1.d0
      gjac(67,86)=1.d0
      
      gjac(68,87)=1.d0
      gjac(68,88)=1.d0
      gjac(68,89)=1.d0
      gjac(68,90)=1.d0
*
      do j=1,n
        do i=1,me 
          k=(j-1)*me+i  
          ge(k)=gjac(i,j)
        end do
      end do
*        
* Constraints. (INEqualities):
*
* Jacobian of the INEqualities constraints:
*
	return
	end                                             
	
*---------------------------------------------------- FP5-3.for